Well, it's not a fuck-up in the timeline. It's a NEW timeline.
Well that's debatable.
The Kirk character in the movie also shares my opinion about how time travel works in his universe.
And the Spock Prime character, if he is indeed supposed to be the same as in TOS, did slingshot around the sun to travel along one timeline.
So even if the Red Matter stuff caused a special case of time travel and parallel universe travel, they would still be able to slingshot around a sun to prevent the destruction of Vulcan in that particular parallel universe.