I think yours is a very interesting question, to which I don't have a definite or singular answer.
From Roland Barthes' perspective, we can turn ANY writerly text into a readerly one by not following its logic, segmenting and re-constructing it in our own way.
Some postmodern texts are more open to this kind of reading--"open" also in the textual sense that they have open endings, offer multiple possibilities, or contain disconnected fragments.
But then do we really reconstruct them in our own ways? Can we really do whatever we want? I don't think so. I still think that the basic purpose of writing and reading is communication, and in that sense, we still want to know what the text says.
Back to John Barth, the non-linear structures of the stories do allow you to jump around in your reading. And I believe you can have a lot of interpretations of what the narrator (say, of "Life Story" and "Title") refer to. However, I believe the number of legitimate readings are limited. And ending(s) still determine a lot.