I'm not sure what you would consider a meaningful statistical comparison, but looking at several relief pitching stats at Fangraphs, Sox relievers are not that bad, except in the category of meltdowns. But even with that, you have to look a little deeper, IMO. The Sox relievers have the highest leverage index (LI) in MLB when entering a game, meaning they are entering in critical situations more so than other teams. IMO, that makes the possibility of a shutdown or a meltdown more likely because there is less wiggle room.
The late inning blown saves and losses are things that will stick in our minds because they are at the end of the game and because they are so difficult to take. We tend to remember those better than the times the BP pitched well.