Dont think thats quite right.....it wasnt that they wouldnt allow him into the First cabin but that they COULDNT....there is no First cabin on the ANU route and there hasnt been for years. Obviously its one of those stories where the sardine becomes a whale as it gets retold.....
Although BA don't sell the "First" product on the ANU routes, occasionally they will operate the service on an aeroplane with a First cabin. When this is the case, more often than not the cabin remains closed, so the whale may be closer to the mark than you think.
