This is why they should have just done a complete reboot for the movie instead of what they did. I'm of the opinion that Star Trek's history doesn't need to follow our history (it is fiction after all and is entertainment), though TPTB always seem to try and make events 'fit' into Trek's timeline. I didn't read the Eugenics War novels and I think the idea of that war being fought 'in secret' is stupid. The war happened, 30+ million were killed and it was a pivotal moment in human history that culminated in the banning of genetic engineering. How a war that kills that many people could be kept secret is absurd and silly.
Khan shouldn't be in the next movie, it would be better to do something else, preferably something new instead of remaking an old movie.