Remember...
This is an altered timeline where the others are already on the ship by the time Kirk gets command of her.
This new timeline doesn't have to conform to the original. It's new.
I mean, I'd have loved it a lot more if they'd kept the promise to "just tell a story that fits into the existing timeline", but now that we know that wasn't true and that the timeline's being changed, then whatever we get from now on is "canon".
Weren't the deaths of Enterprise D's crew an established fact (canon) until Kirk and Picard went back in time and wrecked Soran's plan?
I think the other six regulars could have been on the ship before Kirk even in the TOS timeline, including a very young Chekov (possibly in a temporary posting as a Cadet Trainee) and McCoy. Putting the other 6 on the ship first doesn't violate canon; it only violates "fanon".
There is nothing in TOS that could contradict that, so I think Abrams can say "adheres to canon" and actually mean it without resorting to alternate timelines for an explanation.
I'm still not convinced that alternate timelines will play a huge role in why people's histories are "seemingly" different in this film, because I don't think people's histories will in fact be that different (well, they may be different than "fanon" but they may not be contradictory to canon).