The "Yesterday's Enterprise" timeline is built on the idea of the Enterprise-C leaving the timeline, never being reported as having shown up at the Klingon outpost having (I'm guessing) just "gone missing." So right there it can't be the "correct future" since that future was built on an alteration of the timeline.
Correct. The example I always think of happens in Back to the Future
, when Doc tests the Delorean with Einstein by sending him one minute into the future. For Einstein, the trip happens instantly, and he never realizes that he's gone anywhere. But for Doc and Marty, Einstein is missing for the entire minute that passes before he reappears.
The same is true of the Enterprise
. She disappeared before the Klingons realized that their distress signal had been heard and responded to. They blamed the Federation for not acting properly because they didn't understand what had happened. When the Enterprise
returned to 2344, she was able to defend the outpost from the Romulans long enough for the Klingons to realize that Starfleet was trying to help them.