Without seeing specific screenshot examples of what you are seeing, based on research I would say yes, the DEMs are fine and those structures do exist.
I pulled up Google Maps and took a look at the terrain and satellite imagery from some of the counties you list. Armstrong shows them with the greatest frequency and proximity, for example at https://email@example.com,-101.6107598,17058m/data=!3m1!1e3!5m1!1e4
They appear to be related to agricultural use. The depressions look to be water collection/storage for irrigation purposes. In some cases, particularly examples seen in Randall Co, you'll find them at the center of radially plowed fields using center pivot irrigation systems. Give the arid nature of that part of the country, I can easily see them being made to collect both rainwater when it falls as well as recapture irrigation runoff. They may also start off as natural depressions that are further 'enhanced' by agricultural use.
You might try adding an imagery basemap layer to your map/project, or grabbing some NAIP imagery from the same location to verify/confirm you're looking at the same things.