I was definitely handwaving when I said "in general", but I meant something like "in the absence of local laws to the contrary". And (without sufficiently specifying) I intended to limit my comment to Arizona because that was the focus of the article. Arizona is different than the other Southwestern states. Here's what seems like a more complete overview: https://groundwater.stanford.edu/dashboard/arizona.html

Note that unlike the other states you mentioned, the standard in Arizona is "reasonable use". Texas is the other big outlier. Do you have links (or good search terms) for the recent judgments you refer to? I know some things about this area (certainly enough to call it "complex"), but there is a lot I'm ignorant of.