Quote:
One definition of insomnia is difficulties initiating and/or maintaining sleep, or nonrestorative sleep, associated with impairments of daytime functioning or marked distress for more than 1 month.
Therefore the situation described in the OP would absolutely fall under the category of insomnia. I guess the real question being brought up however is not subtle distinctions in the official definition, but rather...whether some people who think they never sleep actually do sleep a little without being consciously aware of it. I think that's very plausible, considering how much sleep deprivation can affect judgment and memory.