After waking up this morning and seeing the replies to my comment, I realize my answer was not sufficiently nuanced/specific. My first paragraph was in response to the author's explanation on "scientific journal" peer review, which I think is incorrect. But that explanation, for math journals, is reasonable (as pointed out by jdoliner and n09n).

My comments on his papers potentially receiving more peer review was a distinct commment, which does not rely on my qubble with the author's definition of peer review for a "scientific journal". I should have made that more clear in my original comment.