The other issue is OP paid cash only for one of 4 tolls. He doesn't have a problem with being billed for the three tolls where he ran through the Sunpass lane, but doesn't want to pay the administrative fee to Budget. I'm not sure why he thinks Budget should not bill him for handling his tolls.
Don't be so sure it was the Sunpass transponder that paid the toll. In Florida when a vehicle without a transponder goes through a Sunpass lane, the license tag is read and the toll is billed to the car's owner.