That was more down to the Pirellis, I think. Didn't he get a fastest time in qualifying once he was more comfortable with the equipment? (yes i know he had a component penalty and couldn't start from pole). I don't think Schumacher's success falls on one particular factor. Not the one-rooster approach that Ferrari has always followed or the Brawn factor.
But anyway, wasn't Rosberg also the son of a WDC? It could also be said that he was a more complete competitor than his dad, so why write him off so easily? In fact, i think most second-generation professional drivers tend to be more complete than their dads or uncles. With some exceptions, most notably Jacques F. Villeneuve.