Blanket statements are always wrong. Think about it.

I'm having a flashback to logic lessons where we took apart statements like "All the classrooms are too cold." and had to negate it properly. First thing, the opposite of "All" in NOT "None" (any more than "too cold" could be changed to "too warm"). The opposite of "All" is "Not All". Or "Some" (which could mean one because it would only take one room to disprove the statement). And then there was the ever-popular "There Exists a Room Such That ..."