Btw these waiters should have reacted differently. When somebody starts using his strength (shouting, pushing...) you should not allow him to continue the discussion. You literally should just say "STOP!" and show that you are not going to continue like this. Rxplain him in a civil manner that you understand why he is so angry, but tell him you can't divert from your viewpoint because it's YOU who is bound to those rules.
I've been able to lead so many people to reason by just doing this when I worked as lifeguard.