'Severe mental impairment'? I'm tempted to start a list of AB members whom I feel should automatically qualify but I think that I'd probably better not ;-)
More seriously though, the golden rule for any form of benefit should always be "If in doubt, apply for it". As long as everything you put on the application is true, the very worst that can happen is that you'll be refused. (i.e. you can't be prosecuted for attempted fraud).
With regard specifically to Council Tax, it's definitely worth challenging anything that doesn't seem to be right. I was getting a 100% reduction on my Council Tax due to my low income but then, because I started receiving my State Pension, my circumstances changed.
I immediately advised the Council Tax office in writing, providing them with the exact figures for my new income. However they continued to apply a 100% discount to my bill until the very end of the tax year, when they then demanded a year's Council Tax in a single payment (with no option to pay in instalments).
I wrote to my local councillor, protesting that dropping such a large bill in someone's lap (when payment by instalments should have been asked for a year earlier) seemed unfair to me. She managed to get the entire year's bill totally written off for me!