No, even from your clear pictures they weren't able to define the species.
For all the usual reasons, best to stick to a latin name, and as Trichodiadema seems to be the one the South Africans are working with that would be the preference at least in the interim before the Trichodiadema/Mesembryanthum question is resolved - no doubt years away. As John says, crown of thorns would be unwise anyway, as other plants from other families already have the name in the more Biblical sense, most familiarly Euphorbia milii var. splendens, which incidentally does very well for us completely unwatered, in our hot Greek garden (see picture below, taken one January).
I suspect the locals would call it a vygie, but alas that's just what they call any of the mesembs (Aizoaceae).