The quoted explanation is wrong for a few reasons
Most obviously, it disregards current educated usage. So it's descriptively inaccurate. Ignoring that, there is also a problem with the logic of the argument. It rests on an assumption that many cannot be used adverbially, but that seems to be belied by the existence of phrases with "many more", like "many more apples".
In current usage, "many fewer" is more common than "much fewer"
Both much fewer and many fewer are used today in formal written English; apparently much fewer was originally the only form used, but many fewer is more common nowadays.
Consider the examples in (1a-b), which concern many and much as
intensifiers of the quntifier fewer.
(1) a. Nowadays our newspapers carry many / much fewer ads.
b. They had many / much fewer (of these features).
The rivalry between the two is the result of a long drawn out
replacement process leading from the exclusive use of much in earlier
centuries to the predominant use of many in formal written English
today.2 This prompts the following question: are there any
environments delaying or speeding up the ongoing change? Informal
observation had suggested to me that much fewer occured more freely in
cases like (1b), where — unlike the determinative usage in (1a) —
there is no nominal head following fewer. This hunch was confirmed
within minutes by the Google search summarized in table 1. [...]
2 A more detailed diachronic and synchronic analysis of this
phenomenon is under preparation.
("Determinants of grammatical variation in English and the formation / confirmation of hypotheses by means of internet data", by Günter Rohdenburg, in Corpus Linguistics and the Web, 2007,
edited by Marianne Hundt, Nadja Nesselhauf and Carolin Biewer)
The further analysis seems to be in “New Departures”, by Günter Rohdenburg and Julia Schlüter, in One Language Two Grammars, 2009, edited by Günter Rohdenburg and Julia Schlüter.
Rohdenburg and Schlüter mention that "far fewer" is another option, but choose not to compare it with the others. Using databases, they identify two main factors that seem to contribute to the use of "much fewer": it's more common in American English than in British English, and it's more common in both American and British English when there is no following noun phrase. Even in the conditions that are most favorable for "much fewer" (American English, no following noun phrase) it is less common than "many fewer", with only 6 occurences of "much fewer" in these circumstances compared to 16 occurences of "many fewer" (Figure 19.7, p. 372).
As evidence for the historical precedence of "much fewer", Rohdenburg and Schlüter include a citation from Dwight L. Bolinger's Aspects of Language (1968: 127); they say he "writes that 'many fewer is next to impossible' " (Rohdenburg and Schlüter 373).
Other facts that I think are relevant:
"Many" might be an adverb after all. It seems to be used as such in the clearly established phrase "many more"
While phrases like "much more people" do seem to have some use, "many more people" is much more common. The Oxford English Dictionary (OED) has a couple of examples of many followed by mo/ma (an older form of "more") from Middle English, and an example of the exact phrase "many more" from 1559 (W. Cuningham Cosmogr. Glasse). So, "many more" is clearly established in both modern and historical use. The OED suggests that the construction many more "probably arose as an appositive collocation of adjectival many with more (Middle English mo), e.g. ‘there were many, more than..’." This might explain why "many fewer" didn't come to be used until later on: the expression would contradict itself if many is read as an appositive adjective. But this explanation is only historical; the OED does classify "many" as an adverb in the modern expression "many more".
"A little more" and "a few more" are distinguished; "few more" may exist
I tried looking at the opposite case with "more". We do say "a little more [non-count noun]" and "a few more [plural count noun]" respectively. But the indefinite article "a" may make a difference. "Little more [non-count noun]" without an article does exist, but it's not common. I have found an example of "few more [plural count noun]":
you will discover that he has few more ideas than a brute
(The Excellence of Christian Morality by William Bennet, "Appendix" p. 24)
The quantifier "fewer" could be classified as a determiner rather than as an adjective, but I don't think it makes a difference to the argument
Edwin Ashworth left a comment saying
Few/er in 'few/er' apples wouldn't be classed as an adjective nowadays
anyway, so the analysis falls down.
However, I don't think it makes any difference, since as far as I know determiners may require adverbial modifiers just as much as adjectives do. Wikipedia mentions that possessive determiners like "my" etc. can be modified by the adverbs "more", "less" or "(as) much".