U.S. States with Deserts

I thought Oklahoma was one of these for sure

The caveat about desert climate and source 2 are contradicting each other as the Wikipedia article states that Kaʻū isn't a true desert in that it does not have a desert climate with less than 1,000 mm of annual rainfall. I think you should change the caveat.

yeah many places have areas that they call "deserts" but really aren't, such as the Maine desert or the Polish desert. I think the hawaiian desert falls into that category, even though the state does have very barren landscapes. These are due to lava flows that prevent plant growth or some cases high enough altitude for there to be tundra, which you must not consider to be desert because you didn't include alaska. If I were you, I'd use this source:

https://upload.wikimedia.org/wikipedia/commons/c/c3/US_50_states_K%C3%B6ppen.svg

Most of these states have semi-arid deserts (Steppes) but don't have true deserts (under 10 inches of annual precipitation). Also, Hawaii doesn't technically have a desert either.