Well, after waiting two hours (raking leaves... ouch!) I turned off FM Radio, waited 30s, turned it on again, and... silence. Crap. So it doesn't appear to matter if the user has BT on or not (and yes, I know the software says it will turn the BT module on, but it never hurts to check).

On the bright side, I think the "static" bursts I sometimes hear are a side effect of charging the battery at the same time. When the battery's full, the noise disappears.