My guess is it's like saying "Dad met you..." Meaning the speaker's dad. As a native English speaker growing up near London I will say "Dad..." Instead of "My dad..." Uncle could be considered a relation's name like these: Mum, Auntie, Grandad, etc.
Another scenario is if talking to someone to whom the man is their uncle. Like saying to kids "Ask mummy if you can have one." It is not the speakers mummy but the child's.
Might I argue that "Onkelen møtte dere på flyplassen" is also correct for this listening exercise, given that the syllabic /n/ would assimilate into the /m/ for "møtte", so it is impossible to hear the difference?