Stories have always changed with the times. I studied medieval lit at university, so a salient example comes to mind immediately: Perceval, by Chretien. He died with it unfinished, but it nonetheless circulated, and there are no fewer than four "continuations," each quite clearly tied to the original; and further still, Wolfram von Eschenbach based his own Parzival (probably the greatest work of medieval German literature) on Chretien's work.

The only difference in modern times is that we're often leaving the original author's name attached, which is, admittedly, rather insidious.