But an implicit assumption of Bayes theorem is that each new evidence is really "new" evidence that is independent of the evidence that has already been evaluated.

Standing on the shoulders of giants - or standing on the heads of worms. The preceding information influences the future information, regardless of whether it was good information or not.

I guess the mitigation comes through decentralized sources of information, but in a world that is rapidly homogenizing, it is far from foolproof.