It is anticipated that the forthcoming Cherenkov Telescope Array (CTA) will include a number of medium-sized telescopes that are constructed using a dual-mirror Schwarzschild-Couder configuration. These telescopes will sample a wide ($8^{circ}$) field of view using a densely pixelated camera comprising over $10^{4}$ individual readout channels. A readout frequency congruent with the expected single-telescope trigger rates would result in substantial data rates. To ameliorate these data rates, a novel, hardware-level Distributed Intelligent Array Trigger (DIAT) is envisioned. A copy of the DIAT operates autonomously at each telescope and uses reduced metadata from a limited subset of nearby telescopes to veto events prior to camera readout. We present the results of Monte-Carlo simulations that evaluate the efficacy of a Parallax width discriminator that can be used by the DIAT to efficiently distinguish between genuine gamma-ray initiated events and unwanted background events that are initiated by hadronic cosmic rays.