I don't know, I've hooked my G1 up to 2 different boomboxes, 2 different Soloist and I've noticed no buzzing, this while charging it with the AC adapter. It has been noted that some AC adapters will pick up interference, so you may want to try a different AC adapter for charging it. I personally found the ones that came with the G1 and G2 to be cheap junk.
Well then there is little doubt it is ground loop, there are several good group loops kits out there. In my old ride I had to use one, but in my xB I haven't had any issues with ground look, but then everything is factory.