I think all the details matter and I think it is highly likely the officer's affidavit is slanted and contains inaccuracies (not that you have to believe it all in order to believe Beard did enough that you want to stay away from his as the university's flagship hire). It's internally inconsistent and she later recanted.
I'm also pointing out how people think they know the whole story and do not. It's common for people to fill in details using some narrative they already know or one they want to be true. All people do it--trial lawyers exploit and have to defend against this tendency all the time.
Theoretically, here, sure it could be a different thing. For example, I wrestle with my son all the time. Headlocks are common. Putting my hands around his neck like Knight did to Reid has never occurred. Was Beard trying to restrain her from attacking him when he did that? I don't know. Her story after the arrest and his story suggest that is possible. All in all, no matter what, it's an ugly situation and IU would be justified in not hiring Beard because of it. But I don't buy the one-size-fits-all, 100% oppressor v. 100% victim approach to every domestic dispute or man v. woman physical altercation. I admit that might be true here, but I don't know enough to be able to judge and I don't think anyone else does, either.