Actually, I believe that Priceline splits the difference between the minimum rate and the actual bid with the travel provider (I don't know if it is 50/50, though).
Also, I wouldn't be surprised if priceline sometimes processed bids at a loss to them to encourage business.
There is probably also some intelligence in the system so that even if your bid is greater than the minimum arranged with the travel provider, priceline may reject the bid if it is likely that a higher bid will be placed for the same service -- the same logic used to set seat/room/car allocations in the yield management systems used by airlines/hotels/car rental firms.