Been using the government rate as I always have without pushback. I did have one request for ID in the most unlikely of places... a Hyatt House. I provided the ID, but the rate difference would've only been ~$8 extra, so surprised to be asked. Saved a few hundred last night at the Carmel Highlands Inn though.
Half the time I just use my PIV card as my ID off the bat anyway, so I don't need to worry about pushback.