Yep

But then why involve SpaceX in the first place? Unless the point is to just funnel public money into a private corporation?

As crazy as it sounds, SpaceX is the best option out of a bad bunch.

Something that a lot of people might not know is that NASA, except for prototyping, does not and never has built rockets, or crew or cargo vehicles. They build the payloads (like space probes) or supply the astronauts that go into or onto those rockets and crew vehicles. The alternative to the fixed-price contracts that SpaceX now gets are the massive-cost-overrun cost-plus contracts that have historically gone to defense contractors like Boeing, Lockheed Martin, Rockwell, Northrop Grumman, etc.

NASA has historically provided the designs that those defense contractors have built, and sometimes owns the end products (like the space shuttles). This US government aerospace contracting arrangement goes all the way back to the post-WW2 days when the US Army paid Chrysler (yes, the car company) to reverse-engineer captured V2 rockets.