Ahh, but those aren't necessarily the same future! Remember, at the end of "Future's End," Captain Braxton's own history had been changed so that he had never been thrown back in time and had to live on 20th-century Earth. Yet the Braxton of "Relativity" remembered living on 20th-century Earth and had a grudge against Janeway because of it. They contradict each other, which is really just sloppy writing, but it certainly doesn't support your case that they're the same unalterable future.
I think most instances of sloppily written continuity errors in time-travel episodes can be chalked up to the concept of alternate universes. Writers can argue that when characters go back in time to change the past, they aren't changing their OWN past, they're actually creating an alternate universe. Then when they return to their "own" time, they're actually traveling forward into the future of that alternate reality they created. And in their original timeline, nothing's been changed and they've simply disappeared forever. So when Kirk went back in time to save those whales, HIS 23rd Century Earth still got destroyed. But the 23rd Century Earth in the NEW reality he created survives.
I actually think that argument was made clear by Abrams' film and the Countdown comics that preceded it (in which even after Spock and Nero disappeared into the black hole, Spock Prime remembered the universe in which Vulcan wasn't destroyed, and we were shown that the TNG universe we know continued to exist.
So in keeping with that principle, the Braxton who remembered what happened and the Braxton who never did any of it were not the same person; they were Braxtons from two different realities.