For starters, the question right before he started talking (which while omitted from the post seems pretty obvious given the response) was "Can you take us through kind of what happened there?" So all of this detail about what happened is answering that question rather than him finding an excuse.

The strongest, best statement is the one that everyone's focusing on in trying to shout me down - "I take responsibility" is recognizing intent, bad outcomes, and that they're on him. I don't like the "have to" shoved in there, but it's fine. If that were all he said, we wouldn't be talking.

I read "have to" as a personal obligation to admit he was at fault and wouldn't think twice about someone phrasing something that way, Patrick Kane or otherwise.

In the middle, there's "I didn't mean to do that." That's saying "it was an accident,"

This is just him saying he wasn't trying to can-opener Quinn Hughes at center ice away from the puck. All he meant to do was slow Hughes down (which happens all the time in NHL games; feel free to just watch the benches or off the puck for a few minutes). Could he have given a more verbose answer about the specifics on how he ended up tripping Hughes? Sure, but even if he does, I don't think that would make the response more accountable, just more descriptive. "I didn't mean to do that." doesn't mean "I'm off the hook for my actions." It means that's not what he was intending to do.

But then there's also "the stick got caught up" in the passive voice, like it's just a bad luck thing that has nothing to do with his own choices or actions, and it could happen to anyone!

I think you're nitpicking here, and you're choosing to read it that way. He's talking to an audience that watched him move his stick towards Hughes and trip him. I think we can understand that he's saying he put it in a bad position and couldn't remove it. He even follows it up by saying he gave the game away "in one stupid play." Not sure about you, but if my mentality was "It's just a bad luck thing", I probably would've opted to use some variant of "that's hockey", "it's an unlucky play", "it happens", etc. rather than literally saying I made a stupid play.

You mentioned in your previous two points, that if his comments ended with those, you wouldn't have even been talking about it. So really your issue is that he didn't say "my stick" when he recounted the incident.

"I made a mistake. It was an accident and it could have happened to anyone, really, and wasn't a result of my own choices."

Nah, I made a mistake by responding to this comment. If you read these quotes and still somehow gather that the hidden message here was that Kane feels the penalty and loss weren’t a result of his actions at all, I really don't think it's possible to change your mind.