© 2014 American Physical Society. We present a treatment of the high energy scattering of dark Dirac fermions from nuclei, mediated by the exchange of a light vector boson. The dark fermions are produced by proton-nucleus interactions in a fixed target and, after traversing shielding that screens out strongly interacting products, appear similarly to neutrino neutral current scattering in a detector. Using the Fermilab experiment E613 as an example, we place limits on a secluded dark matter scenario. Visible scattering in the detector includes both the familiar regime of large momentum transfer to the nucleus (Q2) described by deeply inelastic scattering, as well as small Q2 kinematics described by the exchanged vector mediator fluctuating into a quark-antiquark pair whose interaction with the nucleus is described by a saturation model. We find that the improved description of the low Q2 scattering leads to important corrections, resulting in more robust constraints in a regime where a description entirely in terms of deeply inelastic scattering cannot be trusted.