I have also read the section from the controller hand book, IMO the word MAYDAY works fine in country's that don't speak English, as an ex-ATC you are trained to fully understand (USA) what the word EMERGENCY means, if he doesn't understand that, he is sure to understand the statement "we have got to get this thing on the ground"
I am not trying to second guess the Supervisors decision but, the problem stands out from the viewpoint of "what if", good that it turned out well.
As far as the nearest runway comment, sounds as if he was tracking from the east and then has an emergency, OK if you have an "emergency" and you are flying over a major airport like Dallas Love, how bad can it be? Just curious.