"to be met" does not mean "to meet."
A prior arrangement whereby someone will go to the airport to collect a passenger
- to "pick them up at" the airport
- to "meet up with" the traveler
-- this is "She has arranged to be met at the airport" or "she was met at the airport."
It means "She was picked up at the airport by prior arrangement."
A: I have to fly to LAX.
B: Are you being met?
A: Yes, someone from the home office will pick me up.
This use has utterly swamped the other meaning of "to meet" when it's used for airport (train station, bus depot) pickups. If you want to say that you made someone's acquaintance for the first time at an airport, you have to add some disambiguation.
"I met my wife at the airport" means that you went there as planned and retrieved her after her flight.
If you want to say that the first time you ever laid eyes on her was in an airport, you'd have to say something extra:
- My wife and I met for the first time in the waiting area of Logan Airport.
- I met the woman who would become my wife when we both tried to take the same bag off the carousel.
- I met my wife for the very first time when we were socked in due to fog at JFK.
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