(from the article): “Any appointments made by an ineligible president would have to be recalled, and their decisions would be invalidated.”
Arguably, this would also be true of his “appointment” of his VP candidate, Biden. Logically, an invalid candidate for president can only select an invalid candidate for v.p.
Biden wasn't appointed by Obama, he was selected by the convention. There is nothing illegal about his candidacy, regardless of what Obama may have done.
The appointment was by the Democrat party not Obama. Biden is qualified to be VP.