There are two parts to this, and one is more troublesome than the other. The simpler part is that the Fed can influence changes in NGDP--the money value of output, or "demand"--more directly than it can influence inflation. The Fed has no control over the way a change in demand divides between higher real output and higher prices. Therefore, it should not be held accountable for the split. But it can and should be held accountable for how the combination of the two--NGDP--evolves.
The trickier question is whether to express the target as an annual rate of change or as a medium-term path. This choice, by the way, has to be made whether you target NGDP or prices. Setting the target as a path aims in effect to claw back some of the fall in demand--or deviation in the track of prices, as the case may be--which happens during a recession. The Fed strives to get NGDP back to where it would have been if the recession had never happened.
The key thing is that with a target expressed as a path, NGDP would need to grow faster than normal during a period of catch-up following a recession. Setting the target as an annual growth rate, with no allowance for the shortfall just experienced, would fold the recession-induced decline in NGDP into a new baseline.