I've become quite familiar with BRG's in the last few months. I believe you said you could get a good rate with a military id. Most hotels and 3rd party providers (like Expedia) will not grant a BRG if it is not generally open to the public. Since the general public does not have a military id your BRG will in all likelihood be denied (same goes for AARP, etc - it doesn't cover the general public).
A great site with lots of info about BRG's is the BRG Blog (just Google it).
As for the Marriott and Hilton - Marriott is great on giving you the BRG - they'll match it and then beat it by 25% (got the Harbor Beach Marriott in Ft. Lauderdale for about $120 this way - this hotel is usually well above $200 / night - in high season over $400 / night).
As for the Hilton, well I'm going to look into filing a class action lawsuit against them (consumer fraud, false advertising). They make it literally almost impossible to successfully file a claim. They keep saying every site is not a match (Expedia, Priceline, Orbitz, etc.) because those sites require prepayment and the Hilton site does not. The only time you will conceivable get a match is if Hilton has an advance purchase rate that is non-refundable and the competing site also has a non-refundable advance purchase rate. However, if Hilton dreams up some other reason they won't honor your claim you are then stuck with the Hilton reservation because it is not refundable.
Stay away from the Hilton, you are wasting your time.