As I understand it repülőtér always takes -re/-en/-rõl

Good question! I wondered the same thing.

I think it's because repülőtér comes from tér (square, as in town square), which Hungarian construes as a 2d object that you stand on rather than in. So whether it's a városi tér or a repülőtér, it's térEN. Though I'm a learner too, so take my analysis with a grain of salt.