Yep. Sounds stupid, but I've seen people try to use a 1 7/8" ball with a 2" coupler and vice versa. Good way to get yourself into trouble.
Guy bought a jon boat/trailer of mine 3 or 4 years ago. Has the wrong ball size (which I told many times before he came) and I tell him there is an auto parts store just around the corner to get a new ball. "I don't need one" he says and he thinks he can make it home about 100 miles away. I urge him that its not going to work. He insists rudely that it will. So I shut my mouth. He leaves and to my surprise he makes it around the corner of my house. Fifteen minutes later here he comes running and knocking at my door asking to borrow my 2" ball because it came loose in the middle of the first busy intersection out of my neighborhood. : ;D