Sort of, but only because of a name technicality. People get into all kinds of silly word games about spiders, because the common names and the scientific names don’t always line up exactly. A purist will tell you that the only spider rightly termed “Brown Recluse” is Loxosceles reclusa, which lives in the Mississippi Valley region of the US, far from Arizona. In Arizona we have a number of cousins of that spider, however, which are other species in the genus Loxosceles. You could call Loxosceles arizonica the “Arizona brown spider,” and Loxosceles deserta the “desert brown spider,” and Loxosceles sabina the “Sabino Canyon brown spider,” if you want to. But they sure do look like the brown recluse, and they have the same kind of venom.