Not only, that, no, they're also a bit of fluff. That doesn't mean they're not also/still the stat block, though...
...until you change it.
Well, no, it's /a way/ that a DM may choose to take. 5e doesn't dictate DMing style, at least, we've heard a lot of talk to the contrary from the designers. Maybe there is a OneTrueWay, and you've identified it, and they're just in denial or applying marketing spin.
But, to be fair, even if one were running in the style you outline, they still might find the final battle with the big bad in question has issues if they stuck with the stat block presented. (Which, afterall, like all 5e rules, is just a starting point...)