To be sure, the movie walla says nothing about "Klingon space". It only says that "the Klingons" are 75,000 kilometers away.
Might refer to the Klingon ships that had previously been giving trouble to the Kelvin until Captain Robau gave them The Look...
I mean, it makes no sense to have the Klingon border be 75,000 kilometers away. That's like your superiors asking if it could be the East Germans shooting at you, and you say no because it's more than three and a half meters from the border... But some lesser Klingon asset, like a ship, could well be 75,000 klicks away and thus unlikely to be the cause of the space thunderstorm. Klingon weapons range in TOS was in that ballpark, at any rate.
I could easily picture a situation where Robau took his ship to investigate something interesting even though the Klingons weren't happy about it, and his crew kept tabs on those Klingon ships in case they decided to act. Who knows, perhaps the Klingons picked up the escape shuttles and brought Robau's crew to Earth (after due complications, of course)?
Timo Saloniemi