There could be a legal obligation placed on doctors to inform the appropriate aviation authority and employer if they consider a patient who works in any safety critical industry is unfit for duty due mental health issues.
A similar situation arises with fitness to drive - you have a duty to breach confidentiality if you believe your patient is driving despite a medical condition (e.g. poor vision) that makes them unfit.
In practice, unless you're a village doctor you're unlikely to see your patient driving about town so it comes up relatively rarely.
There are other situations in which you have to breach confidentiality and I'm fairly sure that if you felt that a patient was 1) unfit to fly and 2) was likely to do so, you would phone up your legal advisers who I'm fairly sure would tell you to breach confidentiality in this situation.
But with psychiatric issues you really don't want to discourage people from seeking help so better to accept that if a patient states they won't fly, you don't go behind their back to their employer.
There could be a legal obligation placed on doctors to inform the appropriate aviation authority and employer if they consider a patient who works in any safety critical industry is unfit for duty due mental health issues. They would not need to specify why that person is unfit for duty.
Think about it: they don't need to say why the person is unfit for duty, but only need to inform them if it's a psychiatric issue? How's that going to encourage people to seek help?
What you could do would be to have a mandatory obligation to inform the employer that they were unfit for duty for any and every cause, without giving the reason. Even and especially a bad cold.