There's not much of a difference, though, between being made immortal and being put in a garden and given the option of eating from the Tree of Life. Adam and Eve could have eaten from that tree at any time until they were barred from doing so as punishment for their having eaten from the forbidden Tree of Knowledge. So the myth explains why we no longer have the chance of being immortal (because of our sinful acquisition of knowlege).

It's sort of a semantic question you're raising, or at least a distinction without much of a difference.