It's not a rights issue. It's a risk management issue and a medical ethics issue. If someone could get sued it's a legal issue as well, and there seem to be a lot of things related to "duty of care" that have not been tested in the courts in the UK.

However, in the UK, Musket's example of a doctor the informing the DVLA of unfitness to drive suggests there is a way of sorting these things out. What happens if a doctor who signs an application for or renewal of a firearms licence sometime later thinks that the person is no longer fit?