Bill Belichick is the greatest NFL head coach of all-time. He has continued to win every year, despite the era of free agency in which personnel changes every year. He has won several Super Bowls, and has his team's in contention in the other years. This year, he has won without his hall of fame quarterback.
A great coach, yes, but to be the greatest I think there must be some lasting impact on the game, some innovation. Paul Brown, Tom Landry, George Halas, and Bill Walsh were probably the greatest innovators who had the greatest lasting impact on the game, not just their eras. Halas brought in the modern pro set offensive formation and he kinda, sorta founded the NFL. Paul Brown brought in film study, the modern balanced offense as we know it, and probably a couple of dozen other things we now take for granted. Tom Landry invented the modern 4-3 defense then turned around and brought the shotgun formation into the modern offense. Bill Walsh took what he learned from Paul Brown and modernized it with the West Coast Offense. Belechick taught us some finer points on cheating and how to reveal nothing to the media.
While Belichick's four Super Bowl rings as Head Coach tie him with Chuck Noll for the most of all-time, he also has the luxury of Brady at quarterback - widely considered one of the best in the game's history at that position. A recent ranking of the "Greatest Coaches in NFL History" by ESPN places Belichick 7th on the list, behind the likes of Vince Lombardi, Bill Walsh, Don Shula, Noll and others.
To claim a coach as the greatest coach of all-time, one would need to look at the records of all the coaches for their entire tenures. Just because his team, which includes more people than just him, won three games in a row, doesn't mean he is the shining superstar. The Coordinators, players, and staff have a lot to do with his success. He may very well be, statistically speaking, the greatest coach, but you can not call him that based on three games in one season.