Maybe, but there are a few catches. Four of the seven league championships were in the All America Football Conference, an independent league which competed with the NFL. The reason that league failed was that Paul Brown easily out-recruited all the other AAFC teams and grabbed all the available talent. The Browns hardly ever lost in AAFC competition, even in the regular season. They won the title in all four years of its existence. (But, when the league went under, the Forty-Niners and Colts joined the Browns in making the transition into the NFL.)
Another point is that Brown minutely scripted the Browns team, even to calling the offensive plays in that pre-tech era by shuttling the offensive guards on every play. Although no NFL quarterback calls his own plays now, it was almost unheard of in the 50s for there to be any other arrangement. Part of the legendary aspect of the careers of Unitas and Starr, for instance, is that they were good playcallers. Although Graham actually had to read defenses and occasionally audible, he never got much credit for the brainy side of the Browns offense because of Brown's overshadowing figure.
Thanks for the walk down memory lane.I forgot how Brown and I think Tom Landry may used the shuffle, to get plays in.
A class act, Graham, may he rest in piece.
Peyton Manning does, and Dan Marino did late in his career. But it is the exception and not the rule.