> NASA is sorta playing the role of a systems integrator here
That used to be the case. For example with the Space Shuttles that is how it went.
With the Commercial Crew Program the idea is that they find commercial providers who take their astronauts where the astronauts has to be when the astronauts has to be there.
One is like building an experimental aircraft from a set of parts. Where they definietly are the system integration. The other is more like paying for airplane tickets.
To quote from the wikipedia page of the program: "The spacecraft are owned and operated by the vendor, and crew transportation is provided to NASA as a commercial service."
> as the ultimate supervision authority to decide if something can or cannot fly.
No. They have the authority to decide if their crew is safe to fly on it or not. But Boeing doesn't need NASA's permission if they just want to fly the Starliner on their own. (As long as they don't fly it with NASA personal, or close to NASA property.)
It is as if you bought a return ticket to fly to some destination and while en-route onwards you heard a death rattle from the engine. Then you have to decide if you trust the company flying you for the return trip, or you find some other way.