Well, in practice, no.
Do you think any corporation is going to bother making a separate model for government contracts versus any other use? I mean, why would they. So unless you can pony up enough cash to compete with a lucrative government contract (and the fact none of us can is, on fact, the while point), the end result will involve these requirements being adopted by the overwhelming majority of generative AI available on the market.
So in reality, no, this absolutely will not be limited to models purchased by the feds. Frankly, I believe choosing to think otherwise to be dangerously naive.