If he wants you to come out on the emergency call again, he has to pay the original emergency fee, AND the next emergency fee for the following call.
My old locksmith instructor Ed Greene would agree with you. He told us a story how a guy called him to unlock his car. He got there, quoted him $20. (Yeah this was a long time ago.) The customer agreed to the price, he went in with the Slim Jim, hooked the latch (NOT the lock button, notice) and opened the door in a few seconds. The customer yells "I'm not paying you twenty bucks for that!" Ed says "Your choice," slams the door and starts walking back to his truck. Customer tries to get into his car and drive away, but the door's still locked...
He says "Hey, get back here and open this!"
Ed tells him "$40.00, please. In advance."
The guy says "Wait, you said $20 before!"
Ed says "Sure, but now I have to do it twice."
The guy paid him the $40.00. What choice did he have, call another locksmith?