Yes, true. So either the doctors lied when they said he went through, or he gave what I outlined above as the "right" answer in spite of what he said to Nora, or my interpretation is totally wrong.

I think Nora gave the wrong answer simply because she tried to answer a hypothetical thought exercise that takes as an assumption that human beings can control their universe. The world of the Leftovers has had a major event show its inhabitants how little control they actually have, regardless of what they believe…

Exactly. Plus, in a world where people vanish and no one knows where they have gone, what living being would have such a level of control? It is a hypothetical that presupposes ultimate human control, while the departure is incredibly strong evidence that such control has never existed.