Given the huge investments NASA has made in SpaceX to date, I'm not entirely convinced that the split between public and private money in this space is as black and white as you suggest.
SpaceX arguably wouldn't be here today without NASA's cash.
NASA paid $1.6b and got 12 flights to the ISS for it. Rather cheap in my book.
I'm not aware of any other "huge investments" ... there were some smaller ones, however.
https://www.wired.com/2009/08/dayintech_0806/