You clearly haven't tried 3.5e, IMHO best edition. Class for every occasion. 362 to be exact, however I might be missing some (ex. savage species monster class progression). And you can obviously mix and match classes as long as you meet the requirements.
I think they're making the claim that if we're looking at "varience", variety, etc. then pf1e has more overall variability. Pathfinder does it with a combination of classes and archetypes, where 3.5e does it with just classes. I don't think they made the explicit claim of there being more classes in pf1e by overall number.
I find that instead of pathfinder having more "classes" by number, it feels more honest about what is a class and what is a subclass/archetype. Imo, many 3.5e classes would be archetypes in pathfinder, as they fit your definition of "instead of x, you get y" without much substantial difference. And likewise, in my experience playing different archetypes in pf can produce vastly different player experiences (some archetypes and classes more than others, for sure).
All of this is pretty subjective, though... and I personally haven't heard anyone making fun of 3.5e for lacking classes, compared to either pf1e or 2e, but it could happen!
3rd sentence, first message.
True, there are few, I wouldn't say "many" tho.
Absolutely they do and I mean, I do like PF1 as well.
I only have a problem with "PF1 has more classes than 3.5", which I would classify as "debatable". I wouldn't say wrong, since some archetypes do change the class enough, to be in my view as well, another class.