Don't know if I got an invite or not. I receive PM's, but I have email notifications turned off. That said, I'm not altogether sure what the purpose of private threads would be. If you only want to include certain members, doesn't the private messaging system more of less accomplish the same thing?
Private threads are where you can upload more extreme pictures and things like that. They are hidden except to the people invited to the thread, even to us Admins unless we look into the thread manually from a forum. But really, that would only happen if we get a message something is against the rules. You have to be Chilli members to use private threads.
It's all very hush hush.
Otherwise of course, just use normal threads.