I have checked near-new M1 rifles from 1940-1941, and the greenish tinge is 1) only on the receiver and certain receiver parts and 2) is in areas such as under the rear sight where no cosmoline could reach. Other parts, like the barrel, op rod and rear sight are black, even though they touch the greenish parts. Any substance applied after assembly would have affected those parts as well, indicating the receiver was dipped separately before assembly.
Plus, M1 rifles were not cosmolined for shipping from the factory; they were oiled and shipped in wooden crates lined with waxed paper.
Jim