First, thank you for your time and reasonable responses, Zero_Kelvin. I appreciate your candor and insights.
"Her work was in theoretical mathematics, on a thesis for which (as she explained to me) this adviser was her only option, at her school. If the work was generic or potentially transferable research, it might make sense that she should be able to simply find another adviser."
Or another school
I noted the "at her school" for this reason. Yes, finding another school was technically an option. However, the difference between "technically" and "practically" is significant. I was never a graduate student, but I know enough about the process to understand that [Boromir] one does not simply pick up and find another school [/Boromir]. The degree of harassment was relevant--it was not a black-and-white matter of violent, physical abuse. This was a real world situation, with all the fuzziness, complexity, and difficult decision-making that goes along with that. It was undoubtedly* harassment, but obviously it was not intolerable for her. I'm sure it crept into their interpersonal dynamic in an insidious fashion, over time, like a slow boil. This is part of the reason that sexual harassment is such a problem, for both the accused and the accusers.
* Undoubtedly to me, based on my familiarity with her as a friend, and on how her story was revealed in bits and pieces, over months/years of our casual conversations. Of course, it would be impractical and difficult to convey this in words, online. My trust in my friend's honesty would never get imparted to a stranger, just as it would be very hard for me to put myself in someone else's shoes in a similar manner.
"Couldn't the university claim that the adviser's offense is not the university's offense?"
IANAL, though I suspect you're probably correct. The question was rhetorical, intended to illustrate some of the uncertainty we faced. It's easy to simply say "No", but that is not the same as seeking answers from a qualified lawyer or legal advocate. That takes time and energy. For a graduate student who is already lacking both, being further drained by such a negative dynamic, I think it's understandable for them to avoid the stress as much as possible. We may be the kind of proactive people who focus on this kind of problem until it gets solved, but I know others (including my two math friends) sometimes opt to avoid the stress of dealing with confrontation or emotional situations.
" Covert recordings are usually illegal/inadmissable as evidence without a warrant
Sexual harassment is illegal where I am from. I don't know about where you live. If it is indeed illegal there she should talk to a lawyer, who can involve the police and secure a warrant for the recording.
Seeking a warrant to gather evidence is a good idea, if that's actually an option. We didn't think of that, probably because of our unfamiliarity with legal process, and because of the time/energy that would take. However, this is part of why I posted about this, so that others facing a similar situation might have the benefit of such suggestions. Thanks!