I'm not sure what data you are receiving, but crews are not deliberately flying the NAT with anything other that 1013 set. BTW, the Strategic Lateral Offset Procedure is not "unofficial".
It is Mode S data, which is downlinking the Barometric Pressure Setting from the aircraft.
The problem seems to have been identifed as concerning Fokker and Airbus aircraft. For these aircraft, once the aircraft is above the Transition Level, the value being sent is the last selected pressure setting used before the Transition Level was passed. In some cases, depending on the pilots altimeter setting procedure, this might be the airfield QNH and thus it will stick at this value until the aircraft descends below the Transition Level again.
A quick look at the radar a few moments ago confirms this. Airbuses have a variety of settings, whereas Boeings, Embraers, and others all have 1013 displayed.