When a supervisor is called on, there is the chance that he/she will write in the record, "Passenger was informed that he can not change the ticket without penalty." (Usually this will happen if the original agent informs the sup along the lines of, "I have a passenger on the phone who insists he speak with you. He wants a waiver, and he won't listen to me....")

Rather, if you simply say, "Thank you," to the original agent, you can call back and start from scratch.