In the distorted wave Born approximation (DWBA), the optical potentials of the entrance and exit channels are constrained by elastic scattering only on the energy shell, so their interior behavior, which a local Woods-Saxon form fixes by convention, is in fact left undetermined. We represent this off-shell freedom through the nonlocality of the optical potential and ask how far it propagates into reaction observables. A unitary transformation of the two-body Hamiltonian generates a continuous family of nonlocal potentials that are phase-shift equivalent, for every partial wave, to a given local potential, while differing in their interior wave functions. Applied to prior-form transfer and nonelastic breakup, the family produces a band of cross sections that share identical two-body elastic observables yet differ appreciably at forward angles. This nonlocality uncertainty is carried by the low partial waves that sample the nuclear interior and is suppressed by the Coulomb and centrifugal barriers, so it is largest for light, weakly charged systems and is expected to be small for heavy ones. The widely used Perey-Buck prescription is not a member of this family. Its nonlocality range is a parameter fitted under the assumption that one energy-independent nonlocal potential serves every energy; freed from that assumption, the range generates a second family that reshapes the interior differently. The off-shell freedom is therefore wider than either family alone maps.