I seem to remember from the early days of the merger, talk of AMG doing some co-branding projects with Chrysler as part of the whole 'synergy' thing. Later, I remember some of the images of the Viper/SLS prototype bearing some subtle Dodge AMG logos embossed in the bumpers. I have no doubt that the two projects were related. Whether it was at first solely a Dodge project, or if it was always a shared chassis, or if it was a pure AMG project is really irrelevant. At the end of the day, the SLS is indeed a twin of what was to be the next gen Viper, which of course says nothing about its worth as a car. In fact, I'm surprised that anyone would be surprised at the link. All three companies specialize in overweight, over-engined vehicles - why wouldn't they cooperate in their efforts?
My guess though, is that AMG 'owned' the project, which was to be a Dodge AMG Viper, and in the split, the project naturally went to Merc along with AMG. I'd go further to guess that Merc taking up the Viper as their own had something to do with their split with McLaren (auto, not F1).