Ok just watched the solution and under glass video. I can't understand the under glass result. Maybe the lack of friction but I thought the conclusion was not conclusive.
This behaves similar to water in a spinning bucket, where center of mass moves upwards.
I'm not sure how to explain this one.
We have a few those PHD types at work. I will see if there are any takers for this question. You can't spin stars. Only bucket. Since you can tell you are spinning or not spinning, spinning or not can't be taken as relative as you move forward and stars move backward.