They didn't say "falsifiable", they said "falsified" -- their word usage was correct: something the is Xifiable can be Xified. "falsified" does indeed mean "proven wrong" -- check your dictionary. (However, they are not correct that the theory of common descent has been falsified. And I have no idea what "Jesus is King" even means, nor is it relevant.)
The idea that there is a tree of sexual reproduction that can attribute for the current variation in genetic material has been disproven. That's where "horizontal gene transfer" theories come in. https://en.wikipedia.org/wiki/Horizontal_gene_transfer