This is not surprising because Facebook treats chat and messages as the same. They both end up in the same thread. So as you can send a message to anybody, you

This is not surprising because Facebook treats chat and messages as the same. They both end up in the same thread. So as you can send a message to anybody, you can "chat" with anybody. Whatever you wrote will be received in their inbox as a regular message. I am not sure what happens with people who choose not to receive messages from the public though.