So, now I ask you, Harv, who was "mentally ill": my grandma who was officially diagnosed, involuntarily confined, and who endured horrible electro-shock treatments? or my grandpa, the respected pillar of his community?
First, I'm very sorry to hear of these situations in your family and realize that these situations had a major impact in your agreement with Alan. However, the situation you presented is not an 'exclusive or' situation. Criminal behavior is a very complex behavior, and it is unlikely that all criminal behavior is a sign of mental illness.
However, there are symptoms of patients that very much coincide to what can be called a mental illness. The fella that I knew obviously became mentally ill. He was diagnosed with schizophrenia, but honestly I think he exhibited Asperger's syndrome-like mentality. In fact, he became a lot like Alan in so many ways (e.g., an infatuation with his knowledge as an infant, emphasis on bizarre thought, etc).
To deny these symptoms are mental illness is, to me, to do what so many family members do. Society doesn't like mental illness. There are unlikely to be visitors in the hospital, no uncontested health benefits, no get well soon cards, and many of the other supporting things done for physically ill people. Instead the mentally ill are encouraged to post on the internet, told that they have an interesting perspective on physics (when it is just their mentally ill perspective encroaching further and further on their rationality), given no confrontation to their economic plight, and maybe even defended in argument against those who are genuinely trying to help them by getting them to face their condition and seek help. This is why mentally illness is being ignored. We as a society do not want to face those exhibiting mental illness and pushing and prodding them to get help. Instead, we ignore the mental illness and ask questions such as 'what do you mean?', 'can you explain yourself', etc. That works for those people who are mentally stable, but for the unstable this kind of serious inquiry only forces them deeper into themselves and more out of touch with reality.
I did face the individual that I discussed with their mental illness. Of course they denied it, and of course they went on to talk about how mental illness does not exist. It is very much a sore subject to me when rational people will sit there with a straight face and enable mentally ill people only worsening their condition. This responsibility is on all of our shoulders. Enabling and ignoring are the sins of those around mental illness, and all too often it is the reason why it is never addressed by society like alcoholism and drug abuse.