My guess would be that at the back of the plane the 10% of normal fare paid does not cover the additional cost
IMHO your guess is wrong, the average commercial passenger doesn't pay the "normal fare" either.. so the "10% of normal" figure doesn't mean a thing. A lot of the time staff pax are paying maybe as much as 60- 70% of the amount a commercial pax sitting in the next seat to them is paying, for a seat that would other wise be unoccupied, so the only cost to BA is issuing an e-ticket, which is pretty much the square route of zero thse days .