One thing that helped me intuit the “sidereal” result (4) was to consider what happens as the radius of circle B approaches 0. At least in my mind, it seems pretty clear that A has to undergo at least one rotation.

That said, I am unsure that I would have caught this as a test-taker. Derek’s videos always have some “trick”, putting me on guard, but in a testing scenario I would have seen the answer for 3 with no answer for 4, marked it down, and moved on quickly.