So basically you have nothing to back your statements up. It appears that when the exchanges break the trade, its completely unwound, as if it never happened. Shares go back to the seller, money goes back to the buyer. No one ends up short.

Nothing you said contradicts what I said. The scenario is that you make two trades - a buy at $10 and a sell at $20. The buy is broken but the sell is not.

Now it's as if you sold but the buy never happened (i.e., you sold stocks you didn't own). That's a short.