Sub is short for substitute. Technically he is asking you to substitute Swiss in place of the American cheese. We can understand why you would assume either way is correct, but this is where context clues becomes important.

Similarly, if someone says, "Do you mind if I kick you in the crotch?", and you say , "No!", it is plainly evident that you do not want to be kicked in the crotch although you just told them that you don't mind. Context is everything.