From the pictures, the stud opposite the missing wheel cover thingy sheared off, so the lug nut and the wheel cover came off the wheel.
I don't think this is the fault of the wheel cover, nor of any imbalance caused by the missing nut. Broken studs in my limited experience usually results from overtorquing, either when installing the lug nuts or when trying to break the free after they've rusted together. There may well be other somewhat common causes. That one has broken does not particularly inspire confidence in the others, since presumably they've been through similar use and abuse.