The price has to be agreed to not only by the buyer, but by the appraiser. If it is not set on data, you may get the seller, but not the appraiser.

It's true that a loan amount/down payment is calculated on sales price or appraised value, whichever is lower, but a buyer is free to pay any price he wishes and bring in the difference in a higher down payment. In an improving market with few listings, we're seeing bidding wars where buyers will in fact pay more than appraised value.