Did my PhD at Princeton, knew Jenny Greene personally (not my adviser though). There is zero conflict of interest in Astronomy generally. No one has anything to gain. Various institutions, Simons included, are just one source of much needed funding. Jim Simons is also a legend in the field, known for Chern-Simons (major result), then founding the medallion fund which netted him billions which he then durned around and used to fund fundemental science. Astrophysics is too low paying for anyone who doesn’t genuinely care about it to do it.

Funding institutions can influence which research gets done, that’s what they do by definition. This can steer people towards and away from various topics or questions, but people will loudly speak their mind if they don’t think something is right. It’s a core tenant of the culture. Go to a colloquia and watch people debate and critique each other.