This is true. Thankfully, I'm doing okay now. But if I weren't, it would be difficult. I have insurance through work that mandates that I see providers who are employed by the same organization. Now for my PCP, I don't really care. It's a big organization and I found a doc in another building in a nearby town. We share some patients in common, but we don't really talk. If I needed counseling? Oh dear. I'd be required to see people with whom I work closely, attend departmental meetings with, see socially from time to time, etc. I could probably go to my insurance and get an exception, but in order to do that I'd have to talk to another colleague who works with the insurance co.
Now if I really felt I needed counseling, I'd either jump through those hoops to try to get an exception (the guy at the insurance co is a good guy and not the judgmental sort) or do self pay with someone private. But it definitely gives one pause for thought. There are also 6 EAP sessions per year and they do have a few contracted therapists outside the organization for just this reason. So there is always that.
My residency program didn't require or specifically encourage counseling. And I think that's appropriate. I mean interventional cardiology programs don't cath all their fellows. I don't think you necessarily need to have experienced therapy yourself to either provide it or know when to refer to it, though it can be helpful. My only concern in programs that use their own faculty would be that I think it would be inappropriate for your therapist to be your supervisor or evaluator. If it's just someone who might give you a lecture or two, that would be okay.