There is possibly, a very simple explanation.... Check in with stolen passport (part of a group, milling around etc etc..... Go through immigration with real one?
There is a thing called a boarding card
I know but i don't think I've ever been asked by immigration to show them my boarding card.. They have only ever been interested in the fact that i have documents and i haven't overstayed and that I'm not wanted for a crime.....But i haven't travelled a lot in Far East.