Anyone can give a checkout. It has nothing to do with FAR's. As long as you are qualified to fly a class/category of a/c you can fly it. You may have done all your training in a C152, but you can walk into a PA-28-161 (Warrior III) and off you go.

The checkout, as said, is insurance driven. It's also driven by the fact that no one is just going to let some schmuck walk in to a FBO and say, "I'd like to fly that airplane, please, I am a private pilot."