It is a normal MEDLINK procedure that when you require a ambulance to meet the aircraft on arrival it will be arranged by MEDLINK. Offcourse only when you have been in touch with them to advice them of the medical problem you have on board the aircraft.
Yesterday we had a passenger who became ill during the flight so we contacted MEDLINK. Their advice was to continue to destination (major UK airport) and MEDLINK would arrange a ambulance to meet the aircraft. No need at all to declare a PAN or MAYDAY.
Can't comment on the BA story because we don't have enough information.
FT