That actually makes a lot of sense. It leverages your own judgement about your friend's judgement and provides potential social consequences for bad behavior.
But the nature of your friendships is poorly captured by Facebook. You can't really tell if people have been friends for 20 years or 20 minutes. Or if they've never met or made a baby together.
There ought to be a simple way to quantify both the "trustedness" of a relationship. At the very least, there should be a "Trust" button underneath every friend's profile photo.
With that info, Airbnb could tell you who your trusted friends trust, which is way more useful.