I expect the reason why the US government currently owns Google is that NSF funded Larry and Sergei's page rank research. ;-)

(Presumably it's the university that actually owns any patents from grad students or faculty [though they do share revenue with faculty inventors I believe] and they in turn license them to Google or other companies. So it's more of a transfer of wealth from the government to universities than to companies.)

Google paid Stanford to license the page rank patent. Stanford executed the research as part of a paid contract with the NSF. The contract did not state that the US government owns the results of the research- Stanford does.

This is an intention incentive created by the government to grow the overall enconomy, rewarding the risk takers (universities that hire PIs that do world-changing research).

Sorry I don't understand how 'Second, most research projects are funded by grants not from the state - it comes from industry and places like that' can imply 'that people really like to lie about this point for ideological reasons'. Can you explain that?

On itself it does not. In the context of thread where people claim exactly that and in the context of hacker news where that particular claim is frequent, it does.