Yes, you're correct. But (there's always a butt), if that contract causes the business to go under, the shareholder loses it's stake in the company. The reason the US didn't take full ownership is because the FED didn't want to show AIG's liabilities (estimates exceed $3 trillion) on it's balance sheet.
Anyways, a shareholder can't invalidate a contract just because they find the contract terms untenable. They invested in the company and as such, were also entered as a de facto party to the original contract. So, while you're correct in asserting that the US taxpayer isn't on the hook in a "legal" sense, for all practical purposes, they most certainly are.
I’m not asserting that the taxpayer isn’t on the hook. I’m asserting that as a shareholder they don’t have any legal right to void the contract.
Others have argued that the tax is just voiding an untenable contract. I am asserting that shareholders have no right to do so (no matter how powerful those shareholders might be). And, since they have no right to void the contract by tax, they are, in essence, imposing a penalty on the beneficiaries of the contract without due process of law.