The only thing that makes for sure sense to me is that letters of recommendation will have more sway at the local school because the adcom is much more likely to know the prof, or at least the rep of the prof.
that's not necessarily true. universities are large, segmented organizations. most universities with law schools have multiple schools/colleges within their institutions (med school, business school, arts % science, engineering, etc.). the assumption that adcoms in one part of a university know professors in another part is unwarranted.
You didn't deal with this modifier: "or at least the rep of the prof."
the reputation of a professor - although adcomms are more likely to know the reputation of a professor than actually know the professor, it's still unlikely that every adcomm at a certain school knows the reputation of every professor at it's own school. there are hundreds or even thousands of professors at every university. the reputation of the most prominent professors might be known, but that would only account for a small portion of professors. there would still be hundreds of professors unknown to adcomms at their own institutions.
but i could be totatlly wrong.