Sort-of answering my own question, at least within the US I'd expect to fight back against any attempt to charge that exceeded the government rate (on the theory that, in so many words, I wasn't "on my own reservation" so much as it was a government-commandeered room that I was being housed in) presuming that the hotel accepted said rate (and I would probably push for that even if they didn't). Below that it would get stickier (I'd probably push back against a "high season" government rate as well). Mind you, I don't travel much outside of North America, Europe, and Australia/New Zealand (my time elsewhere, in my lifetime, consists of one night in Bangkok Singapore, one afternoon in Hong Kong, and depending on one's definitions three trips to the Cayman Islands for vacations over the years).

(Mind you, I'd probably also be looking at how to milk the situation in terms of a chain's award program if I'm at a chain. Put a different way, if I've just had to spend two weeks at your hotel, I'd like to knock that off of my end-of-year/lifetime status chase requirements.)