I know what the author means. He is basing his intuition on this. Which is wrong, because they DO share information, as strategy is played out DURING the game, although it has been agreed upon beforehand.

If they "pass" information, then that means that if player B is after player A in line, then player B somehow gets information about the color of player A's hat. But this is demonstrably false, for the two equivalence classes are the same regardless of whether player A's hat changes colors.

I.e. information is not passed during the game from one player to another. This is different than sharing information ahead of time, and is unrelated to the author's intuition (which is confounded by the fact that the strategy is not measurable).