It looks like Anthropic likely wanted to be able to verify the terms on their own volition whereas OpenAI was fine with letting the government police themselves.
From the DoD perspective they don't want a situation, like, a target is being tracked, and then the screen goes black because the Anthropic committee decided this is out of bounds.
So the governments stance is "We already have laws and procedures in place, we don't want and can't have a CEO to also be part of those checks"
I don't think this outcome would have been any different under a normal blue government either. Definitely with less mud slinging though.
Government's not free to say, "We'll blow up your business with a false accusation if you don't give us the terms we want (and then use defence production act to commandeer the product anyway)". How much more blatantly authoritarian does it get than that?