LOL
IMO Beguile gives an ability/status for target to go back at the end of the turn, like, there's no original player status, only (actual) owner. That becomes copied by the Crusader. But... it's just an idea from me
Similar when you Beguile and Give. Then the card will go back to you, because it's only made to change player and the end of turn, not to "go back".
Still, lol