No, therefore should not be reserved for conclusions beyond a reasonable doubt. It is merely a transition similar to thus or as such:
Therefore, I ordered pepperoni.
Thus, I ordered pepperoni.
As such, I ordered pepperoni.
The extended conversation could have been:
I like meat on my pizza. Therefore, I ordered pepperoni.
You can test for an appropriate use of therefore by flipping the sentence order and using because:
I ordered pepperoni because I like meat on my pizza.
The contention that the therefore segment should be restricted to perfect logical use is forgetting that the word really only serves to draw a causal link between statements.
I like red. Therefore, I painted my wall red.
There is no logic here. I am just explaining why I painted the wall red.
Now, if someone is using therefore as a logical link and the logic sucks, you can say that the argument is bad. But the use of therefore isn't the problem.
This $10 item is 50% off; therefore I am saving $6.
This is wrong, but the use of therefore isn't incorrect because it is simply communicating the thought. The communication is accurate; that makes therefore the appropriate word. Replacing therefore with a different word changes the meaning of the sentence (and could correct the logic) but the intent of the speaker no longer matches the communication.
Edit: Since there seems to be some confusion about the actual definition of the word, here is what my dictionary says:
for that reason; consequently : he was injured and therefore unable to play.
Reason, in this context does not mean "logic". It just means "why".
Why couldn't he play? / He was injured.
He was injured and therefore unable to play.
He was unable to play because he was injured.
It is worth noting that there is a strict logical use for the term therefore that explicitly means something akin to "logically derived from the previous statements" but that would be applicable to formations of the following:
All men are mortal
Aristotle is a man
Therefore, Aristotle is mortal
This is commonly represented by three dots in a triangle (∴). But even in this case, the use of therefore is a signal of a specific meaning. If the conclusion is false, it was not an incorrect use of therefore but simply faulty logic. Removing or changing the word doesn't make the problem go away.