The main driving force is inescapably driven by the intention of the experiment, not natural selection. For natural selection in its true form is without any will or intention to begin with.
The intention of the experiment was to see what (if any) mechanisms would be used so the the bacteria survive their adjusted environments. Dont see how you think that translates into a mechanism that drives evolution? A species wants to survive, and one of the ways to achieve this is to evolve through natural selection. So while the process itself has no will, its is still the primary mechanism behind the evolution that took place in the experiment.
I think the experiment is more about the combination of random mutation and natural selection. While the experiment's protecol of feast and famine emphasises the selection aspect, what is fitter (for selection) is driven by random mutation per generation.