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This is true but irrelevant for causal perturbation theory.maline said:in fact the first term is of order ##e^2##. There are no one-vertex processes, because it isn't possible for all three particles (two fermions and a photon) to be on-shell.
First order means first order in the function ##g## in terms of which the expansion is made, not first order in coupling constants. Your argument does not apply since the parameterized S-matrix ##S(g)## is just a generating function, not an S-matrix in the physical sense. Only the adiabatic limit where ##g\to 1##, has such an interpretation. I added a corresponding remark to my Insight article.