How does Wolverine have adamantium claws in the upcoming movie X-Men: Apocalypse?
It's possible that despite Mystique's efforts, Wolverine was still captured by the Weapon X program and was given the adamantium skeleton.
It's also possible that it's not Wolverine/Logan/James Howlett that we saw, but someone else. Someone like X-23, but with three claws instead of two. I mean that Stryker found someone else and bonded adamantium to their skeleton.