Since they don't mention kidneys, I'd like to see someone apply their approach to this study, claiming that red meat increases the risk of end-stage renal disease:
That's a good idea. As I understand it the Burden of Proof method is a meta-analytical method, though, which means it gets applied to a corpus of studies. I'm sure there are more than 1 study that tries to figure out that relationship, though.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5198288/