What my parenthetical comment that you quoted meant to say (for anyone that was not familiar with it) is thaz ZFC is not some joke, or obscure set of axioms or something irrelevant. Without this remark I thought my comment read that way.
I hope you will agree that ZFC is simply "standard math" - even if its axioms are not referenced explicitly by many working mathematicians.
If this statement requires further refinement let me know. Obviously I'm not a mathematician!