The thing is, it is the Patriots themselves who have won so many Super Bowls that they skew the results. The Patriots have won 6 Super Bowls so you can point to anything NE has done and call that an important ingredient to winning Super Bowls.
If we look at the history before NE's domination, we see countless examples of teams winning Super Bowls without franchise QB's. Chicago (20), NYG (21), Wash (22), NYG (25), Wash (26), Baltimore (35), Tampa Bay (37), Baltimore (47), Denver (50), Philly (52). That's 10 out of the past 35, so it is clearly something which can and does happen.