That is really bizarre. When I bought my first horse I initially boarded him at my lesson barn. From that day on MY horse became my regular lesson horse. After I moved him home, I rode the lesson ponies again every week unless I trailered my guy up for the occasion. I've never heard of such a thing, and would probably be pretty irritated. My guys aren't one-rider only horses, they know that people not me deserve respect, but there are just some people I don't want on my horse! Perhaps I'm selfish.
The closest thing I've ever heard of to your friend's situation is swapping horses in an equitation class. The riders come in and show their horses, and then switch mounts with each other to demonstrate rider versatility. I've never seen it happen, only read of the practice in a few very dated books on showing. Perhaps it's an upper level thing, or just isn't done anymore.