I completely agree with IlPadrino. Heck, I might even ask for it. "Can I have the government rate?" If they give it to me even though I'm not even a gov't employee then that's their loss. If they ask if I'm on gov't business, I'll say no. I'm not misrepresenting anything as long as I don't say I'm a gov't employee on official business.
Room rates are negotiable, and there is nothing wrong with asking for a discount--the AAA discount, the gov't discount, or a discount for no reason at all. Often the rack rate at a hotel is really high, and you're getting screwed if you accept it, so try for any discount you can get. If you don't feel comfortable asking for the gov't rate, just ask if they can give you a discount--you may end up with the gov't rate or AAA discount anyway.
There seems to be a notion in the American psyche that the merchant is the party that sets prices in transactions for goods and services, but in fact, pretty much everything is negotiable (unless prohibited by law--in MI liquor prices are set by the state and non-negotiable).
I was at an auto parts store once and rememberd that a store in town gave employees of my company a discount. I couldn't remember which store it was, and I asked if they gave a discount for Company X. They said, "No, but I can give you a discount anyway." It may be surprising what you can get just for asking.