Hello Catherine
His pyschiatrist would be qualified to issue a fit note, but whether or not they would be willing to I would hate to say. I know they are very busy people, and they may not wish to start going down that route. You could ask his care co-ordinator, but I would be surprised if they have the authority. But no harm in asking! He/she may have some other suggestions.
There is a lady I know who definately qualifies for various awards, but like your son she has very little insight into her condition, and has even sat in assessments and told them that she has no problems. Everytime we have eventually won at appeal, but it is a stressful journey (at least for me) .
I know we always say get evidence to support an application, but in a situation like this it is even more important. Hopefully his care coordinator will be able to write something along the lines that he has unrealistic impression of his own abilities, and then ideally give examples.
Wishing you success,
Anotther Catherine
Nothing on this board constitutes legal advice - always consult a professional about specific problems 
