I feel that there is evidence that it's supernatural ability.
Bardic music (the most similar thing to Dark Knowledge) is Supernatural.
If it's extraordinary it doesn't explain, in any fashion, how exactly one goes about granting this knowledge to my allies (in such a way that the knowledge fades in exactly 60 seconds).
Bardic Music is not a supernatural ability, it's a collection of both Supernatural and Spell-Like abilities. It's really not all that similar to Dark Knowledge at all, either, in terms of mechanics, fluff, or usage. You may as well compare Dark Knowledge to a Barbarian Rage.
Also, just because the bonuses fade after 60 seconds doesn't mean that the knowledge does, nor does there have to be a precise, singular explanation for every little mechanics oddity. You and your DM are overanalyzing the situation. You make a knowledge check, people get bonuses. That's all there is in the text, that's all there is in the rules.