Inside the Actors Studio: Ownership or proctology?

Inside the Actors Studio.
That title needs an apostrophe somewhere.

Is it, “Here is a studio that belongs to one single actor, and we will go inside of it”…? That would be “Inside the Actor’s Studio”.

Is it, “Here is a studio that belongs to many actors, and we will go inside of it”…? Because that’s “Inside the Actors’ Studio”.

Or, disturbingly, are we to the studio in order to go inside of the actors? Because that’s kind of grode. But that’s what “Inside the Actors Studio” means to me. And looking at James Lipton’s expression, I can only guess what it means to him.