I have had BSE and Invisible Shield on ipods, and my phone.
The material picks up the dye from your pockets over time and turn grey/brown/black. It's inevitable. My suggestion would be if the staining bothers you, try putting the phone in a sleeve.
As for peeling off, I think it depends on how it was applied, but once again it will happen. I have had experiences where things start to peel off, and where sometimes it never peel off (on the edges/corners).