Imitation Learning has provided a promising approach to learning complex robot behaviors from expert demonstrations. However, learned policies can make errors that lead to safety violations, which limits their deployment in safety-critical applications. We propose MPC-SafeGIL, a design-time approach that enhances the safety of imitation learning by injecting adversarial disturbances during expert demonstrations. This exposes the expert to a broader range of safety-critical scenarios and allows the imitation policy to learn robust recovery behaviors. Our method uses sampling-based Model Predictive Control (MPC) to approximate worst-case disturbances, making it scalable to high-dimensional and black-box dynamical systems. In contrast to prior work that relies on analytical models or interactive experts, MPC-SafeGIL integrates safety considerations directly into data collection. We validate our approach through extensive simulations including quadruped locomotion and visuomotor navigation and real-world experiments on a quadrotor, demonstrating improvements in both safety and task performance. See our website here: https://leqiu2003.github.io/MPCSafeGIL/