At first I was worried of what would happen if the exchange introduced fake nodes with negative balances at the bottom of the tree, but there would be no way for them to hide that without the first real customer up to the root finding out (there would have to be a negative node that he/she could see). This sounds like a great idea!
Unless the negative valued customer and the surrounding customers never logged in... But thats a limitation of the scheme that can't be avoided. If a user never logs in you could just steal just their balance (and correctly set it to zero). You also must make sure that all customers are seeing the same root, and that you can't do funny business like constantly update it to swap out which customers you're robbing. (e.…
As for the negative values, I wasn't thinking of robbing anyone, but just pretending you are solvent when really you're not. I'm not sure I see what you mean by "swap out which customers you're robbing", could you expand?