That may be true for older Boeings (the BAC 1-11 had a basic "FDR ON" switch on some models). The WoffW function is the back-up path for the 767 at least (or it was when I was in 40-01 Building at Everett). It's only turns the FDR on if the crew haven't carried out the checklist item.
Don't confuse the ON discrete and/or power switching with the Record Inhibit discrete that has to be much more complex now that straight forward g-switches are not allowed to shut off recording. Comes from some incidents where aircraft continues flying for some time after a hard landing/ground impact and then goes down but with no FDR recording.