nope, not silly at all. That's essentially it, in fact. The key step is the expulsion of the aluminum alkoxide to rid the organic piece of one of the oxygen atoms. I'll draw it below the way they drew it in the paper - it's essentially the same, just arrows in a little different order. Aluminum was important, imho, because it can chelate well to give the 6-membered ring, and because it's fairly oxophillic allowing for the key oxygen extrusion step.
So that's part one. Here's part two:
QUESTION (2): While the allylic alcohol is indeed the major (and desired) product, a non-trivial amount of the saturated alcohol (shown below) is formed as a minor (and undesired) byproduct. The authors contend the mechanism which accounts for the formation of the major product cannot readily account for the formation of the byproduct. Rather, they propose that the mechanism forks to provide an alternative mechanism for the formation of the saturated byproduct: that is, one of the intermediates in the mechanism we already have can proceed in one of two directions - the direction we have drawn to give the major product, and a second direction which leads to the byproduct.
Provide a mechanism for the formation of the undesired saturated byproduct.
As said above, the mechanism will start the same, then at some point diverge to give the undesired byproduct.