Well, I make the distance (including the dog-legs via Olney) 160 nm.
What I remembered from the rules about the QXC is that dog legs don't count. It's the straight-line distance between the airfields that count. Fortunately when I calculate those, he gets to 27+55+74 = 156 nm.
After all, if the CAA checks your logbook or blue form with signatures for the QXC, it only contains start and end airfield, not any dog-legs that you may have incorporated, so I guess it makes sense.