Can Hogwarts Make a Mistake?

Is it possible that a Muggle can receive a Hogwarts acceptance letter by accident? Hermione Abbott-Finnigan was raised by distant, distant relatives and had no knowledge of the magical world. She then got a letter in the mail from Hogwarts School of Witchcraft and Wizardry. Most magical little kids feel like it tied up loose ends, or that it explained everything. This was not the case, however, for Hermione.