The signalling in that post is about as clear as it can be.

They’re aggressively signalling that they are cooperative, and that they are not being belligerent. They are using the preferred language and much of the framing that the US government would use, to make it as clear as possible what the key points of their disagreement are, by leaning into alignment on everything else

This is textbook. People are reading this as some kind of confusing, inexplicable framing when it’s how any sensible person would write in their context. When you’re up against an authoritarian regime, that’s willing to abuse all the levers of power against you, you very carefully pick your fights and don’t give them any reason to complain about anything that isn’t essential.

Quibbling about the name of the department would be among the stupidest things I could possibly imagine. As it stands, I’m seeing lots of folks online who generally support the administration saying that Anthropic is correct here. If you gave them a bunch of stupid talking points about how anthropic is being disrespectful, you would lose those people. It doesn’t make sense, they’re obviously terrible people without a soul, but that’s reality.