Wolverine’s mind-bending history

There are tons of inconsistencies with this character alone – but I’ll choose the most obvious one: how he got his adamantium claws in the most recent iteration of the character. I’ll leave aside the ending of The Wolverine, I’ll leave aside the whole Origins thing, and so on.
Thus, in the end of Days of Future Past, he is pulled out of the Potomac by Mystique disguised as Stryker. Still, in Apocalypse, it is revealed that he was actually captured by Stryker, brainwashed, and transformed into the Weapon X. And while this is a better origin story than the other one, it still has a huge question mark hovering over it.
Of course, we can assume that it was another shapeshifter who captured him. But why would I do that? Thus far, in the movie, only Mystique has this ability. And while Mister Sinister will certainly appear, it still makes no sense.
Unless Sinister’s origin is also tampered with, and he isn’t a creation of Apocalypse, as he is in the comics.
