Greaves certainly would not have chased back like they do today, nothing like it, but nor did most forwards in his day. But then it wasn't really expected of forwards until towards the end of his career. He was something of a jack-in-the-box, a real livewire who would come alive the moment there was a sniff of a goal.
But he was also a fine passer of the ball and would play his part in the build-up like any other forward, especially in his younger days. And his hunger for goals meant he would put in a decent enough shift getting into position etc. I suspect his reputation really stems from later in his career when maybe he was more prone to taking a breather. But again, that was not so uncommon in his day. To this day I have vivid memories of Danny Blanchflower frequently bent double trying to catch his breath in his later years.
Different times!