Why does Mirror Entity copy Flightmaster Dungar including the chosen quest?

I have learned that Mirror Entity does not copy Battlecry effects of minions, so I thought it would be perfect to play Flightmaster Dungar into my opponent's ME, but to my surprise their copy also got the flight plan (Plaguelands), even triggering before my own since they started their next turn with FD in play.

This surprised me greatly, since it seems inconsistent with how ME works for all other Battlecry cards.

Is there an explanation or logic to why it works like this?