Second, 'read claims' but not citing them sounds a lot like the hand-wavey 'People are saying ...'
https://www.sensible-med.com/p/cutting-nih-indirects-is-sens...
He also compared the vaccine mandate to the Third Reich.
A very nuanced and balanced individual.
A quick look through his post: he cites overhead from several universities as "luxurious" but doesn't really go in to the specifics of why/how NIH and the institutions negotiated this amount. A lot of what he's complaining about seems more like his personal beef with university bureaucracy, which he tries to tie to indirects, but I think it smacks of someone who didn't bother to pay attention to the "people" part of the institutions he works for vs. the technical part of his work (see related post on linux kernel maintainer politics https://news.ycombinator.com/item?id=43037699)
He is wrong about private foundations with their no-overhead/15-20% cap. These grants are routinely rejected by university contracting; or if accepted, it doesn't really count to justifying a faculty's salary (and hence their future career at the institution) as bean counters do not consider the overhead enough to keep the department in the red/lights on when operating overhead costs are considered. The general gist I got when reviewing foundation grant opportunities were "that's nice, haha, but do this on your own time and not department time".
caycep's given a much more comprehensive response around the logistics & finances, as well as why someone's recent and objectively alarming public statements can (obviously) be used to assess their credibility and impartiality.
If this is the one & only person you can cite as a follow-up of your "So I don't know who to believe?", then my doubts remain.
(Also professors and post docs in many areas can make a lot more in industry, so let's not knock them too much if a university wants to look at least a little attractive to them)
I'm sorry but there's no luxurious facilities being funded with research grant indirects. You've been misled or are mistaken.