I use a long putter myself, and no part of the putter touches my body. My left hand holds the top of the putter, and my right hand grips it farther down, roughly 2 feet lower, which is essentially what Adam Scott does. I've never made a point to notice if he rests it on his chest, but I'm inclined to think he doesn't.
It appears to me that the biggest concern about longer putters in general centers around the use of belly putters, where there's no question that the putter is clearly anchored against the player's body. I could easily envision a change in the rules being adopted that would ban those.