I snagged a govt rate for the Dolphin several years ago, and they asked to see my govt id, but did not request an official govt travel authorization. Got a nice upgrade as well to a corner king room with a partial view of Epcot. They tried to charge me additional for the upgrade at checkout, but after some discussions with the manager, they backed off.
I take advantage of fed govt rates for leisure travel whenever I can (even in Mexico - got an amazing concierge level suite in Cabo for 1/2 price). I've only come across 1 hotel that would honor the govt rate only if on official govt business (a beachfront hotel in Oxnard, CA).