Chegini says he offered to purchase a seat for his daughter in order to make it possible to board the flight; but he was told British Airways does not have a ticket office at the Tehran airport, only in the centre of the city. He says that was not a solution to the issue at hand.
This -> I cannot believe it.
Its not possible to buy a ticket at the airport or online. Maybe this is an Iran-specific issue, but it sounds very very troubling for me.