Do you have a proof that this episode was officially titled this way at the time of its original broascast ?

The Genome doesn't indicate a title for this episode.

Taking in account that the action of this episode took place on December 25, this can be a simple on-screen message setting the time of the action.

The title comes up at the beginning of the episode. I can send you a screen shot if you like.

As indicated, this is an on-screen message to indicate when the action took place.