The clear distinction between private and public is (in my estimation) more of an idealisation of free market economic systems than reality.
In practice, money, power and influence at sufficient scale are the governing system. The idealisation is built on (a) very abstract idealised example (like Adam Smiths charming world of bakers and miller's) and (b) real world examples where free market dynamics work well, the way they are supposed to. For example, much of the SV-2.0 world before the money and politics got to the scale it's at now. But even here, connections always featured prominently at certain choke points like fundraising.
The world of finance in particular is (I feel like I need to keep emphasizing imo, I do not have absolute proofs and I'm speaking in very general terms) more a part of the "public" governing system than the "private" realm of free individuals. Like I said though, I think these terms are not as clear as many HNers do.