I might be able to imitate a homeopath, but I can't imitate a rational, educated, homeopath, because if I thought there was such a thing I would be a homeopath.

Great point!

I guess the point of ITT is that even when you disagree with your opponents, you have the ability to see their (wrong) model of the world exactly as they have it, as opposed to a strawman.

For example, if your opponent believes that 2+2=5, you pass ITT by saying "2+2=5", but you fail it by saying "2+2=7". From your perspective, both results are "equally wrong", but from their perspective, the former is correct, while the latter is plainly wrong.

In other words, the goal of ITT isn't to develop a "different, but equally correct" map of the territory (because if you would believe in correctness of the opponent's map, it would also become your map), but to develop a correct map of your opponent's map (as opposed to an incorrect map of your opponent's map).

So, on some level, while you pass an ITT, you know you are saying something false or misleading; even if just by taking correct arguments and assigning incorrect weights to them. But the goal isn't to derive a correct "alternative truth"; it is to have a good model of your opponent's mind.