A flat approach has potential to increase landing distance only because the pilot tends to flare using the same technique as a normal approach.
if the nose is already higher than on a normal approach, then raising the nose in the usual way would lead to a higher AOA and a potential float.
its easier to imagine it in reverse on a steep approach. On a steep approach a normal flare would lead to a firm touchdown and reduced landing distance
as the energy is dissipated by virtue of the heavy landing.