This is not a criminal investigation. Organizations, even public ones, have wide latitude in how they handle internal investigations as long as they're not making overt public accusations before verifying them.
I'm not saying these kinds of investigations are good. The investigation itself is a punishment. However, administrations have a lot of discretion in future actions, discretion which they can exercise against a professor, without recourse, even when there's no policy violation to cite and punish them for. It's impossible to avoid unofficial punishments, and a punishing investigation process is just another one of those.
I'm also not saying that suspension was a reasonable action to take during this investigation. It sounds extreme for any investigation of comments made by a professor. But I don't know what the allegation was and nobody else is saying what it was. The fact that nobody else is willing to remember on the record what the professor might have said doesn't mean she didn't say anything worth investigating.