as if it portrays some form of documented history
I don't think people are using it in this specific way.
The answer is, the handmaids tale is popular fiction of today. I know the books are decades old but the TV show is what people have "experienced". Additionally, most people's understanding of history is poor.
My education was reasonably good, but we only ever learned about Australian colonial history. I mean we did learn about First Australian's history prior to European arrival but only briefly because not much is known. We also learned quite a lot about the suffering of First Australian's during (and since) the settlement era.
My point is, we did not learn about fascist governments outside Australia.
That being the case this meme is immediately recognisable and carries meaning, while something historic might not.