The CREX and PREX-II measurements of the neutron-skin thickness of 48Ca and 208Pb challenge standard nuclear energy-density functional (EDF) descriptions of nuclei and nuclear matter. We show that the apparent tension arises from an implicit constraint in EDF theory, which ties the density dependence of the functional at the dilute nuclear surface to that of uniform matter near saturation. Relaxing this surface-bulk coupling and independently constraining the dilutedensity sector, while preserving realistic saturation and high-density behavior, yields EDFs that simultaneously reproduce the neutron skins of both nuclei, their electric dipole polarizabilities, and neutron-star mass–radius relations. The established correlation between the neutron-skin thickness and the symmetry-energy slope parameter L at saturation is retained but becomes substantially broader. The results show that current neutron-skin data do not require extreme values of L and highlight an underconstrained degree of freedom associated with low-density nuclear matter.