I’m confused how the “we cannot in good conscience accede to their request” framing benefits Anthropic. Politics 101 would say that you should always leave your opponent a line of retreat.
Do they want to force an escalation with DoW? If so, why? Is this a sign that they believe that they are close enough to RSI that they would win?
They could just not say anything, for example. Or say “there’s a bunch of complex issues we need to work out here, let’s continue the dialog”, hope DoW will agree, and then make a decision a couple weeks from now once the news cycle has moved on and DoW doesn’t lose as much face. Or leave ambiguous what the disagreement is about, and leave room for DoW to pretend it was actually a minor contract dispute that got overblown and is now resolved. Etc.
(I agree though that one possibility is that there are no other options, and the things I’m suggesting won’t work for some reason. E.g. maybe DoW is planning some public thing tomorrow and their only chance was to get out ahead of it.)