When staying on a govt rate, I have been asked several times to show a picture ID documenting my employment with the govt. Unfortuntately, I work for the State of Calif, and we generally do not issue picture ID cards. Then, I'd have to fish around for a business card or letter or meeting agenda which somehow ties me in with my driver's license.
Regarding SET code. I believe that some SET codes also extend to the spouse when traveling. Is that correct? If so, there would not be a tie-in with the company. BTW....when booked with a SET, I have never, ever, ever been asked for any type of ID.
Lastly, yeunganson's question. Some hotels offer a general government rate covering all govt employees. Some hotels have different rates for Federal govt and state govt. And some hotels only allow state govt rates to apply to employees of their own state (meaning, as a State of Calif employee, I could not use a govt rate at a hotel in NY).