Thanks for everybody's replies. When I talked to the front desk, they said the reason why I can't receive points isn't because the room rate is lower ($90/nite instead of $130/nite), but solely because of the direct billing issue.

I, too, thought of getting a copy of my bill and faxing it too the customer service dept., but the lady at the front desk said the only bill she can print up is incidentals, because the room charges are direct billed everyday to my company. argh...