This advice may or may not be coming from personal experience and I have no reason to suspect it's not coming from a good place. That said, usually when programs have you see the program's mental health services, it's not meant to be malignant. I know it's not what the quoted comment says but sometimes, people often naturally have a level of distrust acquired through the process.
In other words, while I won't say it doesn't exist, I don't think it's common for programs to have a psychiatrist evaluate you with intent to identify reasons to dismiss you. Offering mental health services may be a box they have to check. That's the distinction and the point I want to make is that if you're offered mental health services, approach them with an open mind. They're not there to get you to admit you have a mental health disorder or personality disorder so the program can report that to the medical board and get you dismissed (provided you are not trying to harm patients). Their goal is to provide mental health support where possible.
The issue isn't with the simple fact of you seeing a psychiatrist or that the psychiatrist in question does not approach the individual patient with every intention of helping them as much as they can - I will grant you that whatever MH professional involved has pure motives, the issue is that it doesn't change the motives of the *program* in all this.
On the surface it would appear they want to "help" you, but if things are at the point the program thinks you need professional MH assistance, then I would say they probably think your performance is pretty poor, and it's anyone's guess if they feel they can accommodate the time it will take to right a MH ship.
I think we all understand that treating MH issues so severe they are impairing you at work (there is evidence somewhere that many high functioning professionals, it really takes a lot for a clinical diagnosis of say depression to get to a point of say, patient endangerment, typically the issue is that *efficiency* tanks first, and programs, all of medicine, is particularly concerned about that to a point that well I digress), that we would expect that to take some time at least on the order of weeks, for medications or other interventions to have effect.
So again, I wonder the extent this is about help *from the program.* If it's shown you need actual help, then program can say they're not going to accommodate, that they can't. This is not too hard for them to push this line in court, actually. I know this because I've seen it.
If it's shown that you are fine from a MH standpoint, again, that just makes it easier to fire you.
My point is this ABSOLUTELY can be used by a program in a no-win fashion against the resident, no matter how earnest or pure the treating provider.
Now, add in the fact that yes, psychiatrists do have biases when it comes to these things. I know some that are very much on the side of the resident, and others with less sympathetic views. When the PROGRAM chooses the psychiatrist for you, well, can't we all agree it's some form of the worst kind of conflict of interest for someone to have their MH provider chosen for them by their employer or anyone else in a position of regulatory authority over someone, like say a medical board?
Why do you think medical boards and programs do not want you to just be evaluated by the MH provider of your choice and just take THEIR word for how you are doing?? Because obviously you have found someone you feel is in your corner. Because that is generally how people pick their provider.
So while arguably from their perspective the one YOU pick is a less than ideal candidate for evaluating things in an "objective" way in their view, or to take into consideration the objectives of whoever sent you, but if the idea is that YOUR selected physician is not sufficient because they are going to be "biased" by virtue of the fact you chose them... how does this same argument not apply to one chosen by the employer/medical board?
Your point is taken that regardless of who chooses a professional, the odds are that they are a professional and mean a patient well, whatever well means in their view (there is some variation among providers even when all else is equal, just one reason for patients to select their providers), the poster's point that this is rarely coming from a place of the program trying to salvage you vs just check a box to fire you, doesn't make that any less true.
Tldr
Provider motives =/= program motives, and regardless you're probably hosed. Use caution in seeing any provider YOU did not select, and was instead selected by an agent that may not have your individual wellbeing 100% their #1 focus