Huh. Sounds as though I was incorrect about linear methods not working for this. Which leads me to my next point of interest.
If we drop the pretense of "instantaneous load response", as they discuss in that article of slick's, it seems to me that the question should not be "why is load chased in this situation?" but, rather, "surely load is chased in every situation?".
It has long been my intuition that moment distribution is not just an expedient calculation method but, instead, a true description of how load response flows through an indeterminate structure. The handling of imbalances in moment distribution strikes me as too similar to "load chasing" here to be mere coincidence.
Even in an ostensibly determinate structure such as a simple span beam, I feel that you'd still get this "load chasing" at the atomic level as individual molecules rearrange themselves to produce load resistance (equilibrium) while continuing to obey their own version of material law (atomic repulsion and attraction). Every simple span beam is really a gazoolion interdependent, molecular springs after all.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.