A Obviously not exactly as you describe, and certainly not as it is done now.
Current algorithms do exactly the opposite -- prioritize falsehoods. This is because false stories have more surprise value than truth and are more noticed and spread more wildly [1]. The algorithms that value engagement, reading, re-sending, etc. thus raise these stories to the top.
So, on things like climate change, people's reputations, etc., yes, they should behave like the editorial boards that they are, and prioritize content by actual experts in the field and by actual facts. No need to delete everything fake since they can list ~unlimited results, but it should certainly be appropriately down-ranked.
While Google seems to have done a little bit to improve the results for a "flat earth" search, YouTube brings to the top a bunch of videos promoting flat earth BS.
Sorry, but liars, charlitans, scammers, and worse should not be given the same platform and respect as actual experts and professionals.
B that would depend on the content of the letter. It happens much more frequently than you seem to expect. And editorial boards every day exercise exactly this sort of restraint, especially at the more credible outlets: "Are there multiple sources for this?", "Is this actually verifiable?", etc.
In short, to quote Asimov: "There is a cult of ignorance in the United States, and there always has been. The strain of anti-intellectualism has been a constant thread winding its way through our political and cultural life, nurtured by the false notion that democracy means that "my ignorance is just as good as your knowledge."
No, ignorance is not just as good as knowledge and our major institutions (even and perhaps especially commercial ones) should not promote it as such.
[1] http://science.sciencemag.org/content/359/6380/1146.full