ATC will never question the type of emergency call - you can never be over safe. The Mayday or PAN call is between the pilot and the controller he is talking to and there is no "come back" later if it transpires that it could have been a different call.
Once the pilot has told ATC what the problem is, ATC decides the category of emergency for the safety services on the ground. Mayday or PAN will indicate to ATC the priority required and not necessarily the category of emergency action on the ground. If it is down- or up-graded ATC will behave accordingly.