Both versions are acceptable.
If your friend was insisting that you must (as opposed to may) drop the article, then your friend was simply mistaken.
Having said that..
Watching the television is more likely in informal than in formal contexts.
From discussions on this page and from perusing google books, it seems there may be some difference at least in informal usage between American and British English, where American informal usage may favor the version with the definite article, whereas the British usage may favor the version without the definite article in both formal and informal contexts. In fact, there could even be regional differences within the US. (This is how things seem to me at the moment. I admit I don't have a reputable source to back these particular claims up.)
However, the two remarks above are only about tendencies. In no sense and in no context is the version with the definite article 'wrong' or 'unacceptable' or 'bad English'. Indeed, both versions are sometimes found in the same source, sometimes just a few sentences apart (see the examples from published literature at the end of this post).
The discussion below is about some other words as well, not just (the) television. This puts the issues in context and you may start to see some regularities better.
Here is the relevant section of Collins COBUILD English Guides: Articles (pp. 40-42):
6.2 Media and communications
You can refer to systems of mass communication and the media by using a noun with the definite article (or sometimes by using a noun without an article). In this way you can distinguish them from actual objects; 'a radio' will always be a particular object, but 'the radio' could refer to a system, as in this example.
We gather facts and attitudes from the press, the television and the radio.
Words in this category are:
(the) television the box the telephone the press the post (Br)
(the) telly (the) radio the phone the paper the mail (Am)
(the) TV the news the newspapers the papers
When referring to television as a form of entertainment or
communication, you can use the definite article (which tends to be
informal) or no article.
They go on the television and smoke drugs in front of the viewers.
He isn't as serious as he is on television.
The abbreviations, 'TV' and 'telly' can be used in the same way, although 'TV' tends to occur without an article in this sense. 'Telly' is an informal alternative; another informal expression is 'the box'
(always with the).
I don't want to be seen on the telly.
...anyone whose face appears regularly in newspapers and on TV
...a constant background of telly or radio.
If someone says 'on the television' it can mean two things: 'physically on' (There's a photo of him on the television'), or 'being broadcast' ('There's a good programme on the television tonight'). If you say 'on television', only the second meaning is possible. (See
section 6.4 for more information on 'television'.)
You can refer to radio as a means of communication with either the definite article or no article.
I just heard her speaking on the radio.
He had already become a climbing spokesman on radio.
When using 'telephone' or 'phone' to refer to a means of communication, you use the definite article.
A large part of Linda's day is spent on the telephone.
Haig and Nixon are regularly on the phone with each other.
Here we are not thinking of one particular telephone; we are more interested in the form of communication.
There are also the expressions 'by telephone' and 'by phone' in which 'telephone' and 'phone' refer to the system of communication, although there is no article.
...an attempt to reach her at the camp by telephone.
You speak of 'the newspapers' or 'the papers' when referring to
newspapers as a form of media. The meaning is similar to 'the press'.
The papers are saying how unusual it is.
How would it look in the papers?
Sometimes 'the paper' is also used to mean newspapers generally, not one particular newspaper.
This is what we read in the paper.
When you use 'post' (American equivalent 'mail') to refer to a system of communication, you use the definite article.
One morning there arrived through the post an amazing letter.
However, there is also the expression 'by post' which refers to the
He acquired the necessary reference books by post.
Another relevant section is on p. 43:
6.4 Forms of entertainment
When you are talking about someone going to enjoy a form of entertainment you use the definite article with the word for the form of entertainment. Words like this are: 'cinema' (Am 'movies'), 'theatre', 'opera', 'ballet'.
Let's go to the movies.
You have seen things. You have been to the opera, the ballet, the theatre.
Here we are not thinking of a particular performance of an opera or ballet, or a particular theatre building, but just of the form of entertainment.
'Cinema', 'theatre', 'opera', and 'ballet', as well as 'dance', 'film', and 'television', can be used as uncount nouns without an article to refer to the art form.
...supreme artists of dance and theatre.
...a very fine piece of cinema.
Television can be an art medium.
ComGEL (pp. 269-270) refers to this use of the definite article as sporadic reference:
(f) Sporadic reference
5.33 The is sometimes used in reference to an institution of human society. For example, in  there are two possible interpretations of the theatre:
My sister goes to the theatre every month. 
By situational reference, it may mean a particular theatre, say the Criterion Theatre, which my sister attends regularly. But a more likely meaning is that my sister does not necessarily confine her theatre-going to one building: the theatre refers, rather, to the theatre as an institution, so that it would be inappropriate to ask, in response to : Which theatre? We call this the SPORADIC use of the, because reference is made to an institution which may be observed recurrently at various places and times.
There is a similar use of the news, the radio, the television, the paper(s), the press, etc, referring to aspects of mass communication:
Did you hear the ten o'clock news?
What's in the paper(s)/on the radio/on (the) TV this evening?
But with television or TV, there is also the possibility that the article will be omitted (cf 5.45).
The concept of sporadic reference also extends to expressions referring to modern transport and communication, such as the bus, the train, the post (esp BrE), the mail (esp AmE), the telephone:
Mary took the bus/the train to London. OR: a bus/a train
He promised that the letters would be in the post/the mail this evening.
In a temporal rather than spatial sense, sporadic reference may even be taken to apply to the optional use of the before words referring to seasons (eg: the winter, cf 5.47), and to festivals, etc (the New Year, cf 5.67).
[a] The sporadic use of the is in certain instances close to the generic use of the. Compare the use of the theatre in  above with the generic sense of the theatre ['drama as an art form'] in [2l:
She's an expert on (the) (Elizabethan) theatre. [2l
Similarly: the novel, the ballad, (the) drama.
[b] The contrast between situational and sporadic use is manifest in this pair of examples:
There's a vase of on the television (set)/*television.
There's an interesting play on (the) television.
And on pp. 277-278:
Noun phrases with sporadic reference
5.43 We have already mentioned (cf 5.33) the use of the in noun phrases with 'sporadic' definite reference, as in the radio, the theatre. In other cases, however, the sporadic use has become so institutionalized that the article is not used. We distinguish, under this heading, a number of different categories of zero article usage which are 'frozen' as part of idiomatic usage.
(a) Some 'institutions' of human life and society
5.44 Certain nouns have the zero article, especially as complement of at, in, and on in quasi-locative phrases: thus someone may be in church, but not *in library. We call them 'quasi-locative' because, although they appear to have locative meaning, their function is rather more abstract (cf: the theatre, 5.33). In such contexts, nouns such as college, church, etc do not refer to actual buildings or places, but to the institutions associated with them: to be in prison, for example, is to be a prisoner, not a casual visitor; to go to sea is to follow the occupation of a sailor; see the left-hand column below. In the right-hand column we illustrate the same nouns as used with the in situational or cataphoric reference:
town The town/the city is very old.
bed lie down on the bed
be in hospital redecorate the hospital
go to prison, jail walk around the prison/the jail
class (esp AmE) The class works hard.
be at school visit the school
go to sea look out towards the sea
be in/be at church admire the church
go to college the gates of the college
[a] Other related phrases are the following, some of which show variation in the use of article:
get out of bed
during (the) break/recess
be in/return to camp
live on/off (the) campus
be on/off (the) stage
at (the) court [royal palace]; in (the) court [law court]; The case was settled out of court; take someone to court
come/go/leave home; be (at) home; feel at home
With university, the article is optional in BrE in the expressions be at/go to (the) university, whereas AmE requires the definite article (as also with hospital in AmE: 'He's in the hospital.').
[b] The article is sometimes left out also when the reference is to the building, not the institution:
I walked straight back into/to school.
She's at church, arranging flowers.
In AmE, and increasingly in BrE, the article is often omitted in expressions like:
in the center of town, the business part of town.
(b) Means of transport and communication
5.45 This type is confined to zero article following by; but the same nouns can be used elsewhere with 'sporadic' the (cf 5.33):
bicycle take the bicycle
travel bus be on the bus
leave by car prefer the car
come boat choose the boat
go train take a/the train
plane be on the plane
communicate/communication by post (esp BrE)
mail (esp AmE)
a talk on the radio
Jill is on the telephone.
put a letter in the post
send it through the mail
The satellite is replacing cable TV.
Also: by hand
Just as further evidence that what is written above is correct, note that it is easy to find examples of both watching television and watching the television in published literature:
This is to pose our activity in our sitting-rooms, watching the television, as an active process of decoding or interpretation. (source; note that this appears on the same page in the same source as the first example of watching television, below)
GRANDPA: (Watching the television.) (source)
The socio-economically deprived spend a disproportionate time watching the television, an indoor activity. (source)
She just sat watching the television. (source)
It is often assumed (certainly by the broadcasters) that watching television is something done by the family together at home. (source)
We may keep watching television, but the new technologies involve new rituals of use. (source)
So viewers are already accustomed to watching television in nontraditional ways. (source)
Professor Sigman expresses concerns about the amount of time spent watching television. (source)