Peter, the transition of "really" was real, but I don't know if it was debated at the time. The earliest meaning of "really" was "In reality; in a real manner. Also: in fact, actually" (according to the OED). Then later: "Truly, indeed; positively. In later use also as an intensifier: very, thoroughly." As far as I can see, this is the same transition that happened to "literally".