She talks about it in the video in the OP, but apparently her parents ran a private school for the arts. The Kings were looking for something like that to put their kids in. Because of who he was and where they lived at the time, none of the schools in the area would accept their children. The found about the Roberts' school and called them, and they happily accepted the King children. As a result, the two families became friends. Fast forward to when Julia was born, for whatever reason, the Roberts weren't able to afford the associated medical bill. The Kings helped them out and paid for it.