Hotels offering a government rate on the open market are free to offer whatever they want and to restrict however they want. That is why there is no such thing as "the government rate" on the open market and when people ask whether they may book it if they are not on official travel, a state employee, are left-handed, driving a stick shift or, more importantly, why the rate is higher than their per diem, the answer is that there is no single rate.

This is completely different than a specific rate negotiated by an agency for a specific conference where there may very well be prohibitions against kickbacks and the like for meeting organizers and other senior types. E.g., "if I give you the contract for this conference and book 500 rooms with you, will you give me a suite with room service included?" But, that is nothing to do with the question at hand.