My situation was I had a doctors note, but I was misdiagnosed (well, not so much misdiagnosed, as a reason was given pending ongoing investigation) but even now I have been diagnosed, I have been told ESA would probaly argue the toss.
My problem is a brain tumour. Then the symptoms were severe fatigue and clumsiness, but since then I have experienced other aspects like headaches, double vision, sporadic deafness, all caused by a thing growing inside my head.
Now because I didn't (still don't) know if I will live to collect my pension I opted to get my works pension early and just blew ESA out, but even now I am below the savings threshold, I have been told I wouldn't get ESA, or if I did, it would just be at the basic rate. Whatever, I'm getting that amount paid another way now, and have been told I may as well stay as I am.
The thing is, in their eyes I am fit to do something just because I was able to complete tests, and my argument that I couldn't sustain that ability (the more I attempt, the harder it becomes) doesn't wash with them. At home, doing very little, I am exhausted at the end of the day and can barely climb the stairs - if I worked (or even attempted to get to a job) I'd be useless or even worse maybe dead either by an accident because of it or just overdoing it.