Protons are incorporated alongside electrons during the biological reduction of NAD(P)+ to NAD(P)H, as established in biochemical literature.
The claim addresses the incorporation of protons during the biological reduction of NAD. Paper [1] notes that NAD(P)H is involved in proton and electron transmission, and Paper [9] details the reduction mechanism involving electron and proton sources to form NAD(P)H. Both support the claim directly and fully.