A doctor's note for what? You're under no obligation to change jobs and you don't need to prove why. Medical benefits, flexibility in my hours, proximity to doctors, not having to change schools and things like that are definitely considerations for me with jobs. I could have taken much higher paying jobs over the years but these intagibles are very valuable to me. I certainly don't need a doctor's note for my decision though.
Or are you saying that you're on disabilty and volunteering while collecting and you've been offered a paid position but in order to take it you'd lose your disability benefits? I believe that's much more than a doctor's note needed but I really don't know anything about that process. If you know you can't work at a particular place due to your disability then obviously you shouldn't be applying. Did they give you the offer without you applying? Why do you have to prove why you can't take the position? Do you have to prove to your case worker why? Does your case worker even know that you've been offered the job? I guess I'm not fully following your situation.