This and the Pacific-Slope Flycatcher were once considered the same species and identified only as the Western Flycatcher, but the Cordilleran has a different song and his range does not extend into California, whereas the Pacific-Slope Flycatcher, which is otherwise identical, won't be found east of the Sierra Nevadas.
I have seen these Flycatchers every time I've been to the Desert Botanical Gardens now, which has been an ongoing process since August. Because the Cordillerans typically stay in the higher altitudes, the general opinion is that the Flycatchers at the DBG must be Pacific-Slope. However, it's pretty far inland for Pacific Slopes, so it still doesn't seem any more likely to me that it's one or the other based on those two pieces of evidence. The Sibley's field guide doesn't show either coming into the Phoenix area much, but the Cordilleran's summer range, though normally at high altitude, is nearby, whereas Sibley only shows the Pacific-slopes as coming through in migration. Given the options, it seems to me that the likely species is the one that actually lives in the state of Arizona: tie-breaker goes to the Cordilleran.