I played a lot of hockey growing up, and generally the guys that were jerks on the ice were usually jerks off it as well.
So I think what the OP is saying has merit.
I think the "he's allegedly nice off the ice" line is just used by fans to help them disassociate from the fact that they are rooting for a jerk.
We've had different experiences as players then, I suppose. However, on the other hand, I can think of a few teammates or opponents who were both jerks on the ice and jerks off the ice, so perhaps my generalization was hasty.
One of the alternate captains for my junior season of high school hockey was a complete asshole and not a team player by any means, as well as being a jerk off the ice. Incredibly selfish as a player, and felt like he took several penalties per game, most of them stupid and unnecessary, and he didn't like passing the puck. One time he decided to wind up a slap shot from the neutral zone, behind the red line, for no good reason. Needless to say, he didn't score on it. There was also an incident one game where he took some stupid penalty, and I didn't see quite exactly what happened as the linesman was escorting him to the penalty box, but he took exception to whatever the linesman did, and started... punching him. Just... what the hell? Thankfully, he did not play my senior season (don't remember why; he could have graduated that's why, but I don't actually remember whether or not that was the case).
Our goalie was also an asshole. He liked to yell at me (others too for that matter) in the dressing room after games, for random incidents where all I was trying to do was clear the puck out of the crease, and I'd get yelled at because he wanted me to leave it be so he could try to cover the puck instead. Funny thing is that I was kind of young and naive when I started playing hockey, and I was not yet convinced that the concept of "team chemistry" was a thing. That hockey season definitely convinced me that it existed, because the chemistry of that hockey team was just... awful and very dysfunctional. It was almost like everyone hated everyone. My senior season was a lot better because most of the toxic asshole players quit the team for various reasons after my junior season.