Why did Hagrid take Harry to vault 713?

In "Harry Potter and the Sorcerer's Stone," Hagrid takes Harry to Gringotts when he retrieves the Sorcerer's Stone from vault 713. Harry's knowing about vault 713 and its tie to Hogwarts was very much important in his, Ron's, and Hermione's detective work for the conclusion of that book. However, why would Hagrid want to take Harry to Gringotts? Was there some kind of restriction that required Harry to be with him when he retrieved the stone, or was this just done so that Harry would have the knowledge to make the connection between Fluffy, what he was guarding, and the Sorcerer's Stone?