Wouldn't it be more incompetent -not- to at least try to find out whether SpockPrime knew anything about Khan?
As I said above, in a worst-case scenario Our Heroes have nothing to lose.
Yea, shortly after the release of ST'09, so many fans were debating it was Spock-Prime's duty to rattle off everything he knows about BIG dangers that might happen. So, if they didn't go back to the well at some point, there would be complaints that Spock-Prime should've been asked. This way, they addressed it, and showed it had little to no impact (IE: "There, We've done it, don't expect us to go there in STXIII or beyond")
One Day I hope to be the Man my Cat thinks I am
Where are we going? And why are we in this Handbasket?