You asked me a question. I said yes. But it's already clear. I have found the answer. The ball won't start rotating, as can be seen in the. So the question can be closed. I have found more info here. I'll rest my case.We know. And your intuition was developed in a non-relativistic world. That's why we calculate. It appears that you have moved away from asking a question to pushing your point of view: that you intuition is somehow superior to the calculations of people who can do them. Don't go there. Ask questions, sure - convince us that you';re right based on intution? Nope. This is science.
You were presented multiply incompatible options. Which one do you mean? "Yes" is not an acceptable answer.
Furthermore, your intuition is wrong. Consider two concentric spherical shells. Replace the outer shell with a swarm of satellites in circular orbits. This is a zillion Gravity Probe B experiments. Now, set the inner shell spinning. Frame dragging will cause each and every satellite to precess.
From the point of view of a distant observer, the outer shell has gained angular momentum. Where did it comes from? The only place possible is the inner shell. And since angular momentum is conserved (you can add "as measured by a distant observer in Minkowski space" if you like) they inner sphere must slow down. So unquestionably the outer shell exerts a torque on the inner shell.
(This torque is, of course, tiny compared to the torque in launching the satellite swarm in the first place, and for planet-sized objects, the moments of inertia are many, many orders of magnitude larger than the satellite swarm)
My question is did you not even look up the Wikipedia article before coming here and advocating your own wrong point of view? Or did you read it and pretend you didn't because it doesn't support it? I know neither option is particularly positive - I can't help that.
Finally, the question you initially posed is in the section "Lense-Thirring Effect inside a rotating shell" in the article https://en.wikipedia.org/wiki/Frame-dragging;