I am not sure about the circuit breaker ... I have emailed the previous home owners to ask them if some work was done that necessitated putting the Nutone on a separate circuit. I have not found any other light or outlet in the home that is sharing this circuit with the Nutone bathroom fixture.
Here's some pics of both the circuit breaker panel and the opened fixture. I believe that we can see the j-box, but I haven't torn into it yet. The circuit I am using is #4, second from top-right in the box. The writing from someone in the past has written "Bath" and "Nutone" to the right of the breaker. In small print on each of the little toggles it says "20A" and in this case there are two that move in tandem.
Now that you have all of the "plug-ins", unplugged, does the "buzzing" persist, or have you plugged them back in, in succession, to determine the source?