Well, as aljibensis is supposed to be a synonym of perbella, I think we can be pretty sure.
It could be a form of Mammillaria nana, which is a very variable species. The form of this that I have in my collection that is closest in appearance to the plant shown is called M. vergelensis n.n., which is a Piltz name for a plant found near El Vergel.
It is also reminiscent of M. tezontle, whose affiliation is more to crinita, I think, than M. nana.
Sorry I can't be more specific, I find these Stylothelae very hard to be precise about - as I guess many other more learned people have as well, hence the proliferation of names.