Corollary

Gell-Mann Amnesia is:

You open the newspaper to an article on some subject you know well. In Murray's case, physics. In mine, show business. You read the article and see the journalist has absolutely no understanding of either the facts or the issues. Often, the article is so wrong it actually presents the story backward—reversing cause and effect. I call these the "wet streets cause rain" stories. Paper's full of them.
In any case, you read with exasperation or amusement the multiple errors in a story, and then turn the page to national or international affairs, and read as if the rest of the newspaper was somehow more accurate about Palestine than the baloney you just read. You turn the page, and forget what you know.

The corollary is once you've spotted this effect you stop believing anything from a given "news" source, regardless of its veracity.

We've read so many lies about us in so many places I do believe that we conservatives/gun owners/etc... have simply written off the national media for everything.

Contempt is earned.  I have to admit they did the work.