While I don't think a 13 year old can take the place of an instructor, I must bring up the point that a lot of people out there get into horses with no instructors or lessons at all.
I've had horses for close to 20 years and only had my first real lessons in the past year or so. And that's because I have a 3 year old gelding that I am trying to make progress with. But when I got my first horse (at 17) I never had a single lesson. I boarded, so if I had health or care questions I had someone to ask. But not riding instruction.
Maybe it is the type of family you come from. My Dad learned to ride as a kid without an instructor on his sister's spooky horse, bareback without a saddle. So when he got me my first horse AND A SADDLE he figured I was already ahead of the game.
We also took a lot of care in getting a good beginner's horse that was gentle (an Arabian).
So I don't know. Maybe they figure the horse is gentle and the kids will learn by trail and error just plodding around and having fun. Now that I think about it, I really don't even ride with anyone that takes lessons on a regular basis.