I think people misunderstand the term supervision.
When someone who works in an empathetic role, ie a counsellor, psychologist, someone in the church they have the option to take their workload to supervision. That doesn't mean that their supervisor comes on to mumsnet or sits in on their counselling sessions to ensure that what they are posting/advising is right, it means that, every so often, perhaps on a specific basis or on occasions if the need arises, they can go to someone, a supervisor, who is someone also connected with their profession, and offload, as it were.
So say a counsellor has a particularly harrowing case, where a client has been through unspeakable things. Things that are quite disturbing to have to listen to. As a counsellor, you are bound by confidentiality, so you can't go home to your husband and tell them of your day, and that is why you go to supervision, to unburden, so that you are not as deeply affected as you might be otherwise.
I presume this is the kind of supervision that the rev is talking about.