Well aksherly, doctors publish information about patients on the internet every day. Complete with photos.
And they will have asked permission, and if its going in a peer reviewed journal, they can be asked to prove that the patients gave informed consent. IIRC this is one of the ways Andrew Wakefield was found out.
If they're writing a case study, as a part of their learning/education they have to take steps to ensure that any info used is as anonymised as possible. As do Nurses. And I'm sure Physios/OT etc have the same rules and regs. Teachers/ Registered childminders can be reported to OFSTED.
So all of them have something to lose.
I imagine that if it was a one on one agreement, and the other person had nothing to lose i.e...: their registration with a professional body it would be difficult to enforce, unless you had the money to take them to court.
But if its a part of their contract to maintain confidentiality and they don't I can't see why you couldn't sack them.
You could make it explicate in their contract that it would be a sacking offence. But if its in the care of a vulnerable adult/child etc, you would have to acknowledge the 'get out' of if they believe the person is being mistreated that they will not be penalised for reporting this to the police/hospital staff etc.