While that may be accurate, it's still a lot of acerage that is specifically Mojave. At the same time, if I stand on the border of the Mojave in Utah, I'm still in a desert anywhere I go.
If you stand on the border of the Mojave, you probably have one foot in the Great Basin desert that covers the west half of the state. The parent probably simply described or generalized to the wrong desert.
A climate map [1] shows that the only parts of the state which aren't desert are arid mountains; the Salt Lake area has a bit of lake effect snow but that's not in the Colorado River watershed.
