The evidence-free claim here (that with frameworks you end up spending less) is all "vibes"—or, put more charitably, a hunch plus some inductive reasoning. It's not a tested hypothesis.
The crux of your argument* is essentially "a + b > a for some non-zero b", where b represents what you are "paying for your library code". The right side of the relation is supposed to represent using a framework, but this neglects c, the cost paid for not using the Nike method ("Just Do It") when it comes to dealing with things yourself (i.e. the framework cost—which, like b, is never zero).
* as stated at least; it's possible and probable that you really don't mean to say that c simply doesn't exist but that b > c (either by intuition or experience or both) but that's still just a claim—which is the entire basis for the author's criticism: not whether frameworks are or aren't actually more cost-effective, but the greater meta-level concern described here in this comment, in the original piece, and other comments by the author and people like Alex Russell elsewhere describing how resistant the culture is towards the notion of attempting to prove or falsify these kinds of claims (if you can even manage to get people to agree to formulate them in such a way that they can actually be subjected to the scientific method)