I also have used the GOV rate (for leisure travel) many times as well as the AAA and AARP rates and always received all points, miles, benefits and promotions. Agree that GOV rate is often lower than AAA/AARP but sometimes it is much higher.
Suggest also checking Hilton MVP rates. Every once in a while it can be a real money saver compared to all other rates.
FWIW, I’ve found that the Gov rate is often significantly lower when all other rates for a given hotel are relatively high and that the Gov rate is often significantly higher when all other rates for a given hotel are relatively low.