The bigger problem I see is professors that think "Oh well it's sophisticated AI, it can't make a mistake" and take the results for granted.

In one of the twitter thread I saw a screenshot form a professors email where they were mentioning that "X student had 100 more eye movements than Y student" and threatened to fail the entire class.

That email blew my mind because it seemed like the professor just didn't know or didn't care that the software was the problem here. And that's the real issue.

If the email mentioned particular students by name then that in and of itself is a violation (at least in California). We're absolutely not supposed to share any student performance information with anyone other than the student, without permission.

That's federal. FERPA.

Yes, that is exactly how it works (I TA for a class which uses it). Proctorio flags things it thinks are suspicious, and when we look at the video we usually find it was something innocuous (pets are a common culprit). We do find a few people actually cheating though so it definitely has its merits.