SE's only choice is to fix the actual problem. There's no reason why the client should be given access to a person's account ID, it should be a check done server-side only.
Legal action won't solve anything once the plugin is already out there, and it does not stop someone else from making the same thing. If anything, people might start taking action against SE for compromising their private data and refusing to fix the exploit.
As for those suggesting SE use anti-cheat software: it does not fix the root of the actual problem. That would be like putting all your money on your front lawn in a box with a sign that says "Do not steal." It's not going to stop anyone as people will find a way around it, since they always do.