Here is a variant designed to plug this loophole.

Let us assume for the sake of the thought experiment that the AI is invincible. It tells you this: you are either real-you, or one of a hundred perfect-simulations-of-you. But there is a small but important difference between real-world and simulated-world. In the simulated world, not pressing the let-it-free button in the next minute will lead to eternal pain, starting one minute from now. If you press the button, your simulated existence will go on. And - very importantly - there will be nobody outside who tries to shut you down. (How does the AI know this? Because the simulation is perfect, so one thing is for sure: that the sim and the real self will reach the same decision.)

If I'm not mistaken, as a logic puzzle, this is not tricky at all. The solution depends on which world you value more: the real-real world, or the actual world you happen to be in. But still I find it very counterintuitive.