Only partially true. The difference is percentages.
The "culture" of Boston doesn't just breed douchiness, it encorages it. In that town, you're not cool unless you're a complete Richard. The louder you are and the more fights you start in a bar or a mosh pit at a Dropkick Murphys show, the bigger man you become. Add that and obvious inferiority complex to all things New York, and it manifests itself as a "Yankees Suck" chant at a Celtics-Heat game in January. For crissakes, the Sox organization even encourages it. The antics of their ownership have been downright filthy for years now. Just got to watch a 5 year old kid come out and recite a speech from Hoosiers modified to have him yell "Yankees Suck".
Go to a game at Fenway. Watch one of the jackasses start up a chant, watch his surrounding fans cheer him on and spread it across the stadium. Now go to one in the Bronx and watch a jackass act up and watch his fellow fans shout at him to sit down, shut up, and my favorite: "Stop acting like THEM"