This plant has flowers that are snow-white on the tops of the petals, and as the flowers age delicate pink lines appear on the underside of the petals. There are multiple rows of petals (thus ray flowers) and the inner row has yellow at the base; the styles are white, not purple. Also, the basal rosette does not wither away before the flowers appear, and there are a few more leaves (still very scant) up the stem. Unlike skeleton plant, the stems may branch once, producing two flowers/plant.
It should be in the same genus, at least. I have Correll & Johnston, the big fat Manual of the Vascular Plants of Texas, and it's not in there, that I can find. Or in any of my other regional guides.
Since the stem is long, slender, and bare, it sways easily in the wind, making photography of the whole plant even more difficult (against the background available, which is "busy" with mottled cactus, the small leaves and flowers of other plants, it's hard to pick out the skinny stem if you photograph the whole plant....there's too much other stuff and too little stem.
I have six photographs (flower straight on, flower lateral, basal rosette, young plant not yet in flower, stem of adult (worst of the lot), and overall location/habitat showing six or so of the flowers "floating" in the air, which I'm about to email to the plant ID person at the Wildflower Research Center.