I think people that are that picky about their audio should use aftermarket equipment. Some people have some high expectations for a factory stereo system. I think it's better than most any factory system I've heard. If the issue really is the head unit replacing that would seem like a no-brainer, get a new good quality one.
For the record, didn't have any issues with my 07 shaker 500 or my current 2012 shaker 500... everything works great.
edit: read how people are achieving this, engine off in a quiet location with no music and the volume turned on? WOW!! how picky do you have to be to find this? there is an off-button on it. if you aren't listening to it, turn it off. Like i said, if i were this picky I'd just go aftermarket and get good quality stuff.
btw...I have a $5,000 home audio setup that also "has white noise" under these conditions.. LOL!
It's because it's sending what signal it is getting to the speakers. (with no audio present that means any electrical noise there is)
To everyone in this thread: It's working as intended.