In most states the vehicle code stipulates that pedestrians walking along the highway are required to yield the roadway to vehicle traffic (motorized or not). It is legally arguable that paths are highways and that pedestrians walking along them should yield to bicycle traffic, but I don't know anybody in government willing to support this argument.

Where I live, paths were constructed first for pedestrians (many have steps) and later relabeled as multi-use facilities, and then highlighted as bicycle facilities on bike maps. Some of the steps have been upgraded with ramps, but many pre-ADA trailheads and paths remain. The parks departments are unlikely to promote cyclist right of way over pedestrians, and generally discourage fast cycling.