Something NOT to do for xmas!

Little extra benefit/HUGE risk of injury. If you could do this how exactly does it benefit your squat total? Do you often squat in such an unstable environment (if you answer 'yes' then I suggest you change training environments!). You can train balance & lifting separately & get the best of both without the risk if that is your goal. This guy will be out of the game VERY soon after the first failure on this as it's likely to be his last lift ever!
If you want risk, then work up to a big weight on your back, going into the hole with a ton of weight is scary enough for anyone (if there isn't some concern at some point in your training cycle then you aren't lifting heavy enough!). I am impressed by an all-out effort at any weight to be honest in the squat, deadlift, bench press, overhead press or other big lift. This is just plain stupid in my view, the best you're get is ok at balance & learn to lift mediocre weights.
That's my view anyway.

I'm thinking of taking up a collection to bribe the clown on the ball to take down the U.S. flag from the wall of his gym.

Easily tricked, just tell him it's a new FUNCTIONAL stability movement. The flag lower with juggle. What he has to do is stand on the stability ball, juggle oranges in one hand while lowering the flag with the other hand. It is important you only do one rep to get full FUNCTIONAL benefit (every 'FUNCTIONAL' has to be capital to prove how important it is to you ).
Job done, your country less embarrassed!