The impressive capabilities of humans to robustly perform manipulation stems from compliant interactions, enabled by the structure and materials distributed in the hands. We propose that mimicking this spatially distributed compliance in an anthropomorphic robotic hand enhances open-loop manipulation robustness and leads to human-like behaviors. Here we introduce the ADAPT Hand, equipped with configurable compliant elements on the skin, fingers, and wrist. After quantifying the effect of compliance on individual components against a rigid configuration, we experimentally analyze the performance of the full hand. Through automated pick-and-place tests, we show the grasping robustness mirrors the estimated geometric theoretical limit, while stress-testing the robot to perform 800+ grasps. Finally, 24 items with varying geometries are grasped in a constrained environment with a 93% success rate. We demonstrate that the hand-object self-organization behavior, driven by passive adaptation, underpins this robustness. The hand exhibits different grasp types based on object geometries, with a 68% similarity to natural human grasps.