Sorry about the joining the party late...but Warped9 makes some great points.
In ST09, if nuChekov and Original Chekov share the same birthyear, then Chekov should have been 15 in ST09...and obviously he wasn't. The "alternate dimension" can't explain why Chekov would have been born two years before he should have been.
Also, in ST09, Pike is clearly older than Kirk - old enough to be shoehorned into the cliched "father figure" role. In the TOS timeline, he's not much older than Kirk; even in "The Menagerie," Commodore Mendez clearly says that Pike is "about your (meaning Kirk's) age." If anything, Kirk and Pike should have been graduating around the same time, and Pike certainly shouldn't have been that much older than Kirk. How Pike was old enough to be Kirk's "father-figure" in the 2009 movie is beyond me.
One last thing - the alleged "original" Spock claimed that Kirk's father was present when alleged "original" Kirk took command of the Enterprise, but "Conscience of the King" strongly suggests (but doesn't actually say) that Kirk's parents died at Tarsus IV, like Kevin Riley. At least that's what I always concluded from watching that (excellent) TOS episode.
These facts, added to the ones that Warped9 pointed out, make it pretty clear that even the "original" timeline from which the "alternate reality" supposedly branches from is NOT actually the TOS timeline. And that's not even getting into the whole "Kelvin" fiasco...