"Just because you're paranoid, doesn't mean they're not after you"

I'll give you that. It's not a perfect world. Bad s**t DOES happen at work all the time. But, I still contend that encouraging a culture where people are *afraid* to get needed help is counterproductive. Yes, we have a high stakes occupation, and it would suck to have it jeopardized by some douchebag not behaving professionally. But, I'm going to the give the majority of people the benefit of the doubt. But, if I get f****d over, I'll fight it (and yes - you can say that I'm contradicting myself, but this is from my experiences as well).
I don't doubt that this is true. And, you are probably right that I've had the benefit of choosing a non-malignant program. It sounds like the OP is right at the beginning of their experience. I hope they choose well, and it might be good to know early on how their program actually feels about what they put in their contract. Is it just BS that is meant to give the impression of support, or do they actually back it up? Unfortunately, you, I, and the OP probably can't assess that.
I'm not saying that residents may not be coerced into signing the release. But, if the records are being accessed without your consent OR knowledge, they should be ready for possible legal repercussions.
I, too, had to take some time off during residency for a medical leave, and also required my medical clearance from ALL of my providers (including my mental health provider). Several folks, including occupational physicians that I was rotating with and discussed things with candidly, mentioned that it would be potentially illegal for aspects of my training contract to be changed on the basis of medical leave. On the other hand, if I was found to be significantly impaired and should not be caring for patients, regardless of whether or not that fit in with my career goals, I probably shouldn't be practicing, right?
I didn't say that such things NEVER get around. I'm said if your mental health compromises your work, that will be spread FASTER.
If someone sees you waiting in the reception area for the psychiatrist's office, that's gossip, speculation, and not really anyone's busy (but some nosy nebs will still choose to make it their business, and yeah - they could spread it around, even it's not true - maybe you were waiting for a meeting or an interview?). It might eventually permeate your entire workplace, but that's a sign of a toxic work environment to begin with (and yeah - you don't need to tell me that most hospitals are like this, I know). But, I'll bet that gossip train is a whole lot slower than the "Dr. So-and-so is incompetent" one. And, if the "rumor mill" train comes around after you've already gotten back on track, most people won't give a s**t if you're doing a good job now. (How are these train metaphors working for you?)
It doesn't help them, but that's not because of my actions. It's because of the other person that doesn't understand professionalism. And, by doing something about it, you are trying to make a small chip into the "unwritten curriculum" that everyone acknowledges but mostly unwilling to try to change.
True enough. But, unless we're living the lives of the saints and have not a single skeleton in our closet, that's a risk that we face every day. Someone could point at a resident's facebook page and suggest that they have an alcohol problem because of "one too many pictures" that they were unwise enough to post.
I'm just arguing that, whatever the problem is (mental health and substance abuse are the points brought up so far), suggesting that people do not seek out help when it's needed is ultimately going to result in a bigger problem than "maybe the other residents are gossiping about me". And, if your PD is pulling this kind of crap, you might already be screwed and other people need to know that this stuff needs to be investigated. But for the individual, going without help has a better chance of leading to a serious negative outcome, either a professionalism issue (working impaired, stealing narcs, fraud, whatever) or worse (not excluding death).