I was thinking of the movie Tangled and it strikes me that the King and Queen have no reason to believe that Rapunzel is their long lost princess. Pretenders have popped up throughout history claiming to be for example one of the princes who disappeared from the tower of London or the Grand Duchess Anastasia. So how could they possibly know or believe that this girl is in fact their daughter. This can extend to other stories as well as it is a common theme in literature to have a long lost royal.
Magic hair? Her story.
No magic hair by that point in the story. Since the King and Queen never speak in the movie, you just have to rely on the Disney magic of a mother knowing her child.
The tower. Ostensibly no one else in the kingdom knows about it, if she shows it to her parents and tells them the story that might convince them. She can also describe the witch who the parents saw.
In this particular case, although certainly not conclusive evidence, there was an exceedingly strong maternal resemblance, both in appearance and mannerisms.