I think the majority of such claims are misunderstandings of "generates downforce equal to its own weight" which is most certainly not enough to drive upside do

I think the majority of such claims are misunderstandings of "generates downforce equal to its own weight" which is most certainly not enough to drive upside down. The only case of a manufacturer actually wanting to perform a test was Gumpert with Apollo, according to Top Gear UK (take it FWIW).