Did you not have travel orders? I would have allowed the desk to copy those as those prove you are on government business and are entitled to the discount and the tax exemption. While I know many government employees use the discount for leisure purposes, I believe that this is technically illegal as fed employees, at least, are not entitled to receive personal discounts for being a government employee. Of course, many employees have very liberal travel orders ... I could see the hotel not honoring a government rate if you could not produce travel orders.

The IDs I'm familiar with - again fed - are security IDs and must not be copied.

Edited to add: Just saw this addressed above. If you do not travel on orders are you really entitled to government rates? All employees of the fed agency I'm familiar with have orders, and many of those are very broad (covering full year at a time and any location). They may also pay with their own cc and be reimbursed, as also noted above.

I'm surprised DOD badges still have SSNs on them. FAA took them off long ago after much identity theft.