[Spoiler Alert]
I presume that the clip takes place after all of the X-Men and Wolverine movies. This is because Wolverine has his bone claws but still asks to be patted down at the airport, meaning that he still has adamantium in his body. This will therefore follow on from the events at the end of The Wolverine movie. Additionally, we know from the film that this takes place sometime after Wolverine killed Dr Jean Grey (Phoenix), which is after she killed Xavier.
However, the clip shows Professor Xavier as alive even though we saw him explode in X-Men The Last Stand and Magneto loses his power in the same film, but in Magneto's case we get a small glimpse of his power potentially coming back. This is how the debate really started, if the clip is after all the films then why can it show Professor Xavier in the present day?
Could it be mind trickery and everyone saw what the Professor wanted them to see?
I would like to know what other people think, please leave a comment below