It's not a cactus flower, I thought it might be adenium obesum, but that's an African/Arabian plant and didn't look right to me. The person found it growing from hard packed earth, and called it a "desert rose." But that might not be the actual common name. I'd appreciate the help.

If you go to this site and click on the link under the photo, you find a show of 12 desert flowers. Might be one of them is that one, you are looking for ( my favorite for your research is number 12:
http://www.berkeley.edu/news/media/releases/2002/06/14_desert.html
And here are some more:
http://www.1000wordsphotos.com/desertflowers/index.html
http://tchester.org/plants/lists/calif_pix_and_db.html