you can't use whatsapp web when your phone is not on the same network
All bets are off, now that it's FB's beast, but the two device solution was intended as a privacy feature, afaik.
I sat next to Pasha Sadri, the web client lead, for 4 months before the acquisition. He mentiond the problem a few times.
The fact it took another 2 years to get the client out seems to indicate that multiple problems were solved in other ways.