Not true. There's a restaraunt in my town (and not even a very large town!) that pays all staff the same (relatively decent) wage and splits any tips they do happen to get equally among all staff. Obviously people will still tip, because that's the culture here, but if you didn't tip it's not like the staff won't be paid at all.

Places like that are rare but they're out there, and the principled thing to do would be to spend your money with establishments that are doing their best to be part of the solution.