Actually, this varies widely by hotel and by government entity, regardless of your opinion.

Part of the challenge is that there isn't one Marriott corporate answer. A hotel adjacent to a state capitol building might have a specific contract with one government entity for a set rate and number of rooms that requires it to strictly enforce a provision requiring an ID and a form-letter authorizing use of the rate.

A different hotel miles away from any major government installation might choose to load a generic rate under the "government" bucket and offer it as a small courtesy discount to anyone attached to any form of public service.