He has done it before yes, but at a club he had plenty of experience at beforehand. He took them up, he was the manager who got them into a position where they could go up and have a fighting chance of staying up the following year. Pearson was also the manager who up until the turnaround last minute was taking them straight back down and had been 'sacked' just before it. I highly doubt he could just walk into a job and keep a club up just like that, especially one like sunderland's.
Plus the other angle is that what manager could they get now, pearson included, would they want next season in charge? Perhaps they even see moyes as a long term manager to regroup them and rebuild the squad if/when they go down? Perhaps they will have someone in mind and they wouldn't be the right man to keep them up like this?
Maybe they know they are going down already and aren't going to be gambling so much on something they don't believe is possible?
Just a few thoughts on it all.