The ad says the inquiry is the result of political pressure and not based on "any prior formal complaint of specific professional or academic misconduct on his part."
The emphasis is on PRIOR. The professors are claiming that, if they speak up, then it would be improper to investigate their past academic credentials and conduct in any way that wouldn't have happened if they hadn't spoken up. I disagree. By stepping forward and making a prominent statement, I think it is fair for people (especially other academics) to ask "who is this guy, and what are his credentials, and what has he done before?" In the course of that scrutiny, things may come to light. If you have major gaps and misconduct, you may want to think twice before attracting attention to yourself. Does that put your freedom to speak under restriction? Not if speaking is more important to you than the possible consequences.
On the other hand, who of us is perfectly clean? Who doesn't have something in their past that they would prefer to remain unnoticed? Where the line is between fair scrutiny and gratuitious character assassination, I don't know.
If it were only one comment or one issue with Churchill I don't think it would have escalated to this level. But he continues to reinforce his hate-America rhetoric through paid university appearances. He's been found to lie extensively about military background, ethnic heritage and possibly his academic credentials. He's been discovered to copy and sell artwork as his own. He assaulted a cameraman and they have it on tape.
Added up, there is more than enough reason to investigate him. Getting close to police investigation time IMO and not just the university.