Since I don't know what Lamb would say to your criticism I will just make a guess. I think that your setup is somewhat artificial in the sense that the light beam is seriously modified (i.e. totally absorbed) in the electronic emission process. In the photon model, your light beam would carry a few photons assuming it was at the relevant frequency. I think this is not the situation Lamb intended to address. He was trying to model what I assume was the experimentally relevant (at the time) situation of a semiclassical light beam containing many photons.Scientifically, I don't think the statement is too naive at all. Lamb and Scully produced a model that violated conservation of energy. If a classical flash of light comes along with an energy equal to 1.5W, where W is the work-function of the metal, then conservation of energy dictates that the number of electrons ejected through the surface is either 1 or 0. Lamb and Scully's model says that with quite high probability, the number of electrons ejected will be 2 or more. Since nobody has been able to produce a model that simultaneously (1) has a classical electromagnetic field, and (2) satisfies conservation of energy, I think it is absolutely fair to say that the photoelectric effect suffices to prove the quantized nature of light.
Of course, I agree that energy is ultimately conserved. But I like to ask myself how important it is to keep track of this for the decription of the experiment in question. I think Lamb regards it as relatively unimportant in this case.
My personal opinion is that it's bad to teach students that one experiment proves or disproves something. I think we know by now that this just isn't how science works. It may nevertheless be how science is taught. I appreciate your frustration with black body radiation, so perhaps a more balanced presentation of multiple experiments is better?Educationally, what I really abhor is the textbooks that introduce the photon via blackbody radiation. It's a horrible mess to try to get that across to students. And what are the advantages? Scientifically, it's not any better than the photoelectric effect, because either observation suffices to prove that light is quantized. Historically, it's also no better than the photoelectric effect, because Planck didn't interpret his calculation in terms of quantization, and the success of his calculations was no more successful than the photoelectric effect in convincing people like Bohr.