Re: My Greivences of Nutrek. What makes me a hater...
They weren't looking for Khan. They were searching deep space for anything that they could use. They stumbled upon him just like Kirk did.
Remember the bulk of the fleet is on the side of the Federation in the Laurentian System
for some reason that we really not a reason for. So there was something going on that we didn't know about
The Federation could a little more paranoid in this universe and constantly scanning space. Even in TOS, their relationship with the Romulans is tense. In this universe, a Starfleet ship encounters a vastly superior Romulan ship and gets attacked for no reason. The only thing that saved the survivors is the actions of George Kirk. I doubt they would buy the Romulan Empire's excuse that it wasn't their bad, it was some jerk from the future. That is if they were even able to make any sort of contact with them. Later Kirk mentions that saving Nero could lead to peace with them. So there may be an ongoing conflict with them at this point. This gets made worse with the destruction of Vulcan and the attack on Earth and a decent portion of the fleet. The Federation is likely on the brink of war at this point and looking for any future attack.
Then they happen to stumble upon Khan and his frozen pals.
"Libertarianism is a good idea on paper, until you look at it."
Greg Proops, The Smartest Man in the World