Surely the carrier is in a position to know where they boarded
I don't think you understand what is actually happening.
When an Asylum seeker arrives on a particular flight having destroyed his papers, he/she loiters in the terminal for a while before going through immigration.
When he/she gets to immigration they then claim asylum and give as their departure point some country in turmoil - the immigration officer is unable to check what flight they came in on as half a dozen flights or more may have landed between the time they got off their flight and when they presented themselves at immigration.
As the immigration officer cannot determine their point of origin he has to allow them into the system and give them the train fare to Croydon.