1) Generally it is surely possible that NATS have made a mistake - everybody does. Would not expect it to be too often though.
2) The HR phone number is to be found somewhere, I remember calling them like three times.
3) The HR are quite helpful over the phone, they are usually able to tell you which part you failed or how bad it was. (Not sure about stage 1, surely so with the stage 2)
4) I wouldn't be that surprised over a fail in stage 1 - quite honestly, that's where most people get fired. (Both in numbers and percentage.)