Funny... I just read the WIKI article on the subject of RTFM and they don't know what the origin is.  I don't either but the first time I heard it was way back in '71 right after I got out of boot camp.  Seems like the military was the source for a lot of colorful expressions that "civies" never even heard of. 

For example, I nearly died laughing when Harvard Graphics came out with their advertising campaign based on "For your next dog and pony show".  "Civies" just don't have a clue about that one.