Other mistake: Flynn and Rapunzel go through the Snugly Duckling tunnel. Later when Maximus points to it, you could easily see it from anywhere in the pub. But nobody saw Flynn and Rapunzel go through other than the thug who showed them.
Other mistake: When Flynn and Rapunzel are in the tunnel and the guards are coming, when the guards turn the corner, you can't see the 70 feet of her hair, and she's not carrying it before that.
Other mistake: Rapunzel's hair is somehow attached to the top of a tree and she is suspended off the ground, swinging in circles around the tree. However, her position relative to the ground does not change. As she repeatedly swings around the tree, she should be getting further above the ground. Also, her hair inexplicably never gets caught or snagged in the branches of the tree.
Other mistake: In the boat scene, when Eugene takes out the lanterns, Rapunzel is moving way too fast compared to before and after.
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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