I never knew it was the "Murray Gell-Mann Amnesia effect" but I've been using this exact line of reasoning for many years when discussing the validity of stories read and watched in the media. Interestingly I discovered it as a kid reading a newspaper article about video games something I was very much into at the time. The were talking about the Sega Genesis and the Super Nintendo and at least half of the article's "facts" were just flat wrong and many of the opinions were far left field of what a legitimate gamer would really think. That's when I made the connection. If this story which is something that I am intimately familiar is so utterly wrong then...what about the things I don't know about. That was about the time I stopped paying so much attention to the general media.
I didn't know it had a fancy name though.