Absolutely. Never talk to me either. Never talk to the professor. Tell them "an investigation is better as it will prove your innocence and resolve the issue more quickly then my explanations will" and walk away if you did cheat. If the prisoners dilemma all over again especially since it takes 2 to cheat in most cases.
> For instance, when I was an adjunct, I didn't have support like that from my department.
I'm different in that I'm not a professor, I help teach and grade a class so I work underneath a professor who allows me to lecture some times and help guide the class but it's not "my" class. As a grader I see all the students work and as an attentive grader I memorize the students names and styles. When I catch a cheater I email my boss and the professor I work under and they advise me on what to do (which is usually to allow me to write my strongly worded letter of doom that anyone who's done something iffy on the internet has received once or twice). The policy in this programming class is that it's not cheating if you credit each other with parts of the work you've done but the less astute observers won't remember that and will try and hide their work.
> What I don't know is how I'd have reacted as a college student with less confidence and street smarts, and with a possibly justifiable fear of antagonizing a teacher.
Some of these kids are in other classes I'm taking and they are still afraid when I bring it up. It's the fear that I will involve the administration that works here. The carrot or the stick. They assume I'm the carrot and I'm going to just mark them zero if they fess up. They assume that the school is the stick and they will get the full penalty.
If it were up to me any cheating would be handled officially through the university but that isn't our SOP. We find cheaters usually fail. As such we just tell them "we know and we are going to give you a 0 for this and next exam". That usually deters cheating as they need to retake the class then.