Look at it this way, beyond the obvious HYS... most law schools benefit from the visibility of their undergraduate programs. Tulane is up there, in the top 50 -- in terms of undergraduate... American is a little more under the radar, down in the 80's.
Also heres a good observation for you. "National" perception of schools may be driven by their prominence on an NCAA sports level. Look at Tulane, and their football team... American, nothing.