When I was around 15 or so, my Mum must have had lots of work colleagues with kids as I remember often being farmed out to someone's house I didn't know to look after their kids for the evening. Bearing in mind, at the time I had very little experience with kids and would not have known how to react if anything happened (besides calling for help!), this didn't phase me... infact I clearly remember one time looking after 3 under 10's being more nervous about the possibility of their huge pet lizard getting out of it's cage!
Did you babysit when you were a teenager? Would you let a teenager babysit your LO's? Maybe times have changed, but I don't think I'd be comfortable with it, unless it was a family friend I trusted and knew really well. For all I know, it could be illegal to let an under 18 supervise children now.