No it doesn't at all. Private corporations shouldn't be telling the government what it can and can't do. That's the job of the people. You want private corporation overriding your vote?
So Google can't tell the government it needs a warrant to perform a search? Google can't sue over something the government did?
It's Google's product they want to buy.
now follow orders.
And again, it's Google's product. Why can't they set conditions? If I pay Google to host my email, I'm still subject to their policies.
(Yes, I recognize that past military entanglements do read as favors for Big Oil, but that’s more because lobbyists directly purchased the corrupt and useless Congress)
A mechanism to address this exists, though.
https://en.wikipedia.org/wiki/Defense_Production_Act_of_1950
The main issue here is that Congress is asleep at the wheel and has refused to implement any sort of guardrails around how the government is and is not allowed to use AI.