You are correct, there are cases where "currently" carries a shade of meaning over "now." The author is not saying never to use "currently." He's saying that in

You are correct, there are cases where "currently" carries a shade of meaning over "now." The author is not saying never to use "currently." He's saying that in cases where either are ok, use "now." English diction can give some very dense and precise meanings (try reading Poe!), but often people use the longer word simply because it's more ornamental rather than because of its specific connotations. This tends to hurt more than help, as many of his examples show.