That's right, I hear a very slight hiss pretty much static noise coming from the speakers as soon as I turn the keys and the Bose system is off.
I hope it's simpler than a pinched wire somewhere. not feeling like hunting it down..

 

Is your system entirely stock?

 

Mine does exactly the same. . Full stock.

 

Still haven't addressed this issue, I'm not the original owner but everything seems stock.

 

I too noticed it on my stock Bose system. I have the Navi as well if that makes a difference.