Continuity mistake: Just before Flynn cuts off Rapunzel's hair, there is a shot from behind him and he reaches up with his right hand to push her hair behind her ear. His arm is visible up to his forearm and the shackle is nowhere in sight. However, in the next, wide shot, the shackle is suddenly up around his wrist. (01:01:20)
Trivia: Pinocchio is sitting in the rafters above Flynn Ryder during the "I've Got a Dream" scene.
Answer: It's entirely possible. Rapunzel has a similar face appearance to her mother's, and you could also count the family bond of simply knowing. She also has green eyes, which are uncommon, so the parents probably knew that she was unlikely an impostor.
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