I thought that the lone wolf concept meant that the individual acted without the organizations or other members realizing it. So, it's nothing to do with one person "going crackers", as you call it, just that he took the initiative to act.

The fact that the Islamic State took responsibility for the action may or may not be true. They may have decided to so so after the fact. or, as it is meant to appear, they may actually have sent one individual alone to accomplish this deed (which seems unlikely, doesn't it?).

And as it happens, Marc Lepine was another such person who acted alone, though he claimed to have been engaged in the war against feminism, which suggests he was not alone in his ideology, though he did turn out to be alone in planning and carrying out the Montreal Massacre.  He also wrote about what inspired him, and it was revolutionaries, I believe.  So, my point is that a person may feel they have connections with a particular group, but that group may not feel the same.