The boards seve several purposes. !st strength. They are screwd to the Rafters not the weak roof shingles. Second they provide air space so when roof sweats it drys underneath -metal can sweat.3rd tney provide a sound barrier for rain and other noise.
SDure you for go this and save as in any construction you can save by not doing it right.The best way is strip the old roof put down a sound insulation barrier and use the 1x4 and do it right. But since its an apartment building for rental money we know it will not get done right.