So you actually believe that if we imagine two plumbers A and B doing exactly the same jobs at exactly the same speed, A charging 70$ an hour and B 35$, A is twice as productive as B ?

It's in line with GDP based reasoning but that's generally done on aggregated data which tend to smooth out these kinds of oddities. As a direct comparaison, it is probably at odd with what most people envision when they think of productivity.