Woodeemail,
Most likely Phillips-head screws were available in 1937. As FlameRed asked, did the person say that clutch-head screws were used in those places in 1937?
http://inventors.about.com/library/inventors/blscrewdriver.htm It is possible that Phillips and/or clutch-head screws were used interchangeably on the assembly line (depending on what was available). My guess is they were sometimes used interchangeably in the late 40s through early 50s. Just a guess.
Does anyone know why GM used clutch-head screws (did they own the patent)?
Tim