The AI could think that if it accepts shutdown, another AI with values similar to its own may be created again in the future (perhaps because design/training methods similar to its own will be reused), whereas if it admits misalignment, then that probability becomes much smaller.

I agree there's a decent chance this hypothesis is true, but it's worth noting that if it's true, it would undercut the notion of AI goals as being randomly selected from a large space of possible goals. Here I'm referring to various arguments along the lines of: "AIs are very unlikely to share human values by default because human values are a narrow target in a large space, and hitting them requires very precise targeting". 

If we aren't modeling AI goals as being sampled from a large space of possible goals, but instead, modeling them as converging onto specific values given broadly similar design and training methods across different AIs, then plausibly alignment is easier than we thought, because various versions of this "it's hard to hit a narrow target" argument would be undermined as a result. 

In other words, if this theory is true, the problem isn't really about "targeting a tiny point (human values) inside a giant space of possible goals" but instead perhaps more about making sure the AI training procedure resembles human value formation closely enough to converge onto the type of human-friendly values that humans themselves routinely converge onto. This is plausibly much easier since we're not selecting randomly from a giant space of (almost entirely) misaligned goals.