I had a suspicion, so I spent a few minutes digging. These are the stats from Fergie's last 6 seasons in charge. Results after the first 4 PL games:
2007-08: 1 win, 2 draws, 1 loss
2008-09: 1 win, 2 draws, 1 loss
2009-10: 3 wins, 1 loss
2010-11: 2 wins, 2 draws
2011-12: 4 wins
2012-13: 3 wins, 1 loss
Even with Fergie in charge in our most successful era, our starts were never great. The only time we managed to win the first 4 games we also failed to win the league. And after the worst start on that list, we arguably had our best season ever.
Moral of the story: the first month of the PL is a bit weird. The players aren't fit, new players need to adjust and odd results always happen.