This is just like car sales. So you go into a dealership and say you will buy there. They say the price they offer you is only good until you walk out the door. They won't give you their "best price" without it. Now, will the price still be good if you go out the door and come back? Maybe, maybe not. Assuming the car is still on the lot, if you come back, they will see someone else has not topped the offer, and may reconsider whether their original offer was too high.
Is this fair? depends on whether you are the dealer or the customer.