Who's to say that there isn't a large duck on the Enterprise? It could be the kiddie swimming pool with a slide down the neck. No reason there couldn't be.
Some people, like Christopher, go for the broad strokes approach. The stories play out pretty much as we see but some of the details are a little fuzzy. Me, I prefer the "everything happened as we saw it" approach. Just because we can't work out all the hows and whys doesn't mean that we have to gloss over parts of it. ""It's a big galaxy Mr. Scott" Expand that idea to a multiverse and there's more than enough room for all the various stories, even the ones that appear to be contradictory. No need to rewrite the past. Make a copy and make your changes there. Was Khan a product of eugenics or genetic engineering? Yes to both, depending on which universe you're in. Why did the Enterprise-A travel to the center of the galaxy in a matter of hours or days when it would take Voyager decades to travel the same distance. Different universe with different laws of physics, at least where FTL travel is concerned.
The whole idea of a prime universe which somehow sits above all the others is so limiting. No version of approved Star Trek is better or worse, more valid or important than any other. Enjoy your episodes, movies, comics and books. Fit it together however you like and don't worry about what someone decides is or isn't part of the whole tapestry.