I think the problem might be that he is using 0 for n1 and 1 for n2. Those are the lowest energy levels in the quantum mechanical quantum theory, but not the Bohr theory (where the lowest levels are n1=1 and n2=2). The equation wouldn't give the right answer with n1=0 and n2=1, so you have to use the lowest levels from the Bohr theory.
Hope this helped.