Quite a few of these people are PhDs, e.g. the physicist Giovanni-something. They usually have an astonishing grasp of math

Ah, yeah, another common problem with people who are good at math from other fields trying to comment on economics. Econometric theory isn't just math. It's a close connection between math, the underlying economics, and how your assumptions tie the underlying economics to the math. I find that people coming from a physics/engineering background often fail to grasp that. Because they are used to modeling physical systems where the underlying assumptions are natural law and (afaict) 100% accurate to how the world behaves. Not so for economics/finance.

As someone with both a physics and econ background, I like to offend physicists by saying econ is harder than physics. (Because of the assumptions issue, but also because of some self-referentiality in what we do. How people think about econ actually affects how the economy behaves. But how we think about physics doesn't affect how nature behaves.)