I remember that podcast, and here's my understanding of what was going on.
In A Christmas Carol, the ghosts appear to Scrooge in the order of Marley (Progress), Past, Present, and Future, and actually represent those concerns of influence over Scrooge. For that story, it is not only a matter of presentation, but the chronological order of events and points made within the story. Changing the order of appearance of the ghosts to Scrooge (what Jim was doing*) is a structural change, not one of weaving.
However, if the events of the story are maintained in exactly the same chronological order, but only presented differently, then it would be a change in story weaving. That is, keep the order of the appearances of the ghosts to Scrooge as in the original (Marley, Past, Present, and Future). However, show us, as audience, Scrooge's experience with Future before, say, his experience with Marley. Since Scrooge still sees the ghosts in the same order as in the original, their influence on him remains the same, as does the structure.
The story maintains the same internal order (structure), but the presentation (weaving) is given out of order.
*I think Jim did this because the software doesn't allow an IC Signpost order of Progress, Past, Present, Future. Thus, the experiment was quite intentionally about changing the structure of the story, the actual, internal chronology of the appearances of the ghosts.
P.S. There is a movie constantly referred to on here that severely messes with the story weaving, but I don't remember the title. I think it was either Momento or Pulp Fiction, but don't quote me on that.