Sorry to reanimate this thread. I just want to comment on a few things.
I think I see the problem now: I'm confused by the fact that Possession has in effect created a new trigger. ("...any of his cards that are trashed are set aside and returned to his discard pile at end of turn.") Normally, triggers "you control" and that "happen to you" are coming from the cards you yourself play. But I think DXV is saying that these new triggers, created by another player, will still "happen" to the possessed player.
I'm happy with this answer, but I think it still creates a precedent whereby triggers can be applied to other players besides the one who plays them or has them in hand.
I disagree with your original claim that this ruling sets a new precedent. The Possession card creates several triggers: After this turn, the player to your left gets another turn (which you see/control); when he would gain a card, you gain it instead; when he trashes a card, he sets it aside; and the trashed-and-set-aside cards are put into his discard at the end of the turn. This is of course what you are saying in your latest post, quoted above. There is nothing in any rule or ruling that says that triggers can only apply to the player "creating" the triggers. In fact, Embargo does this too, with the Embargo token.
As others have said, the card is actually trashed. "When-trash" effects can only happen when a card is trashed. And they happen
after the card is trashed. Possession's effect (setting the card aside) is a when-trash effect. The only thing that isn't entirely clear on the card is whether the trashed card is set aside at the end of the turn or immediately. But first of all, why set it aside at the end of the turn if you're going to return it to the discard straight after that? Logically, it's clear that the point is to set it aside as you go. Second of all, this is explained in the rulebook FAQ anyway.
I don't think that "trashing" and "moving to the trash" are the same thing. I think that the event "card X is trashed" triggers the subsequent event "card X is moved to the trash pile". It's sort of like how the event "I buy card X" triggers the subsequent event "I gain card X".
"Moving to the trash" doesn't appear anywhere on any cards. It's just a way to explain what happens when you trash a card. It's moved from where it was to trash. So it has nothing to do with the buy/gain thing. If a card
did say "move to trash" however, then it would be like "put into discard": it wouldn't trigger when-trash effects (like Drab Emordnilap said).