as far as I can tell from my own investigations into it, Murray Gell-Mann did not coin this term or have much of anything to do with it. Murray Gell-Mann himself was a quantum physicist and I don't think he spent a lot of time worrying about the news media.
I believe the "Gell-Mann Amnesia Effect" is something created by the fiction author Michael Crichton as a plot device. It may be an interesting idea but as far as I know it is not a real researched effect in media studies or psychology.
the name "Gell-Mann Amnesia" was, in fact, chosen by Crichton self-consciously so that this false impression would be more likely in discussions such as this one. Lack of context and a fancy sounding name serve to obfuscate the truth here.
I'm not sure it's worth defending against people taking a fancy-sounding name and taking that as an indication that it's scientific principle without even bothering to take five seconds to look it up.
Sturgeon's Law is named after Ted Sturgeon, a fiction writer, who actually basically coined the phrase originally (I think he did anyway).
Michael Crichton, on the other hand, did not call his idea "Crichton's Law of Media Analysis". He deliberately gave it an obfuscatory name and attempted to associate it with a well regarded physicist to give the impression that the law was scientific in some way. It was a deliberate misdirection, done for effect.
Because of the intrinsically duplicitous nature of the name "Gell-Mann Amnesia" I think its inappropriate to continue referring to the effect under that name. Call it Crichton's Law or whatever. Lets not repeat the original misdirection though. It is fundamentally dishonest and does a disservice to the legacy of Murray Gell-Mann.