Mine always had the nut on the right and that doesn't make sense. You ride forwards, the axle will turn in the direction that the wheel is turning (not that it should!) and if it did the nut would loosen and eventually fall out because mine doesn't even have a retaining pin or something like that. I swapped it over so the nut is on the left, it's also a lot easier getting the wheel back on if you put the axle in from the right side. I don't see any good reason why you can't swap it, my neighbour's TDM has it with the nut on the left too.