They can display (if they are not DEXes) though any arbitrage bot will be triggered literally in milliseconds to sell at that price, in which the exchange eithe

They can display (if they are not DEXes) though any arbitrage bot will be triggered literally in milliseconds to sell at that price, in which the exchange either has to authorize the trade (so it really is at that price then) or fail the transaction with some error which would instantly smell fishy.