Many years ago my mother told me 'If you want to hear your favorite song, don't tip the monkey. You have to tip the organ grinder'. So I suggest that you call CUETEC.
In one of the versions Fats missed a shot on purpose and it wet in the wrong hole. Maybe a 3 rail bank. Do you remember the shot? When I saw it 50 or 60 years ago I thought it was great. Then later on I saw it again and thought it was easy.
I think the rule should be stated either always yes or always no. The contestant should not be allowed to call a foul on himself. He shoud be able appeal the decision though. It just gives the opponent another way to shark the game. If a contestant can make the decision...do away with referees.