Your second paragraph is correct and may be where the previous poster's intuition was disagreeing, that the method doesn't necessarily hold for repeated iterations in a physical system where one trial starts from where the last one ended.

It's not even really "spooky" - all you need is a flipping apparatus that's biased towards an odd number of rotations, and so then THTH is more common than THHT and you get a bias towards repeating your last result.