If you think the policy is too broad and covers more than just these extreme examples, I'd love to see a rule that only covers such extremes and can't possibly be abused.
So, to answer your question, the regulation could sanction people convicted of violent offences when the violent offenses pertain the the university and/or it's members. Therefore:
"The university reserves the right to sanction members of its community who have been convicted of acts of violence, or convicted of making credible threats of violence, against it's members."
"lower standards of harm and evidence" are used because the consequences are lower. As the importance of an organization grows, the standards grow. At the lowest end of the spectrum, you don't need any evidence or process to kick someone out of a house party, because the stakes are very low. At the highest end, you need a ton of evidence and process to kick someone out of society by imprisoning them, because the stakes couldn't be higher. There's a big spectrum in between - banning someone from a store/sports stadium/airline, kicking someone out of a professional organization, firing someone from a job, etc.
I don't know the details of UofO's process, but I do think it's appropriate that they have lower standards and faster responses than a criminal prosecution.
You're correct. Digging deeper, I find no mention either. The title is factually incorrect. I will make updates to my comment to reflect this so as to avoid providing false information. That said, this sort of action is still deeply concerning given that someone can now bring social media posts and speech to the attention of the university for sanction.