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No, the "narrative" is not based just on Clinton's claims. There's way more than that. There's research into fake social media accounts, what they do, and who runs them. To me, the one that really stands out was when sock puppet Facebook accounts organized a BLM rally and a MAGA rally at the same time and place. That seems pretty clear what the intent was.
The quality of evidence for this idea (really, this conspiracy theory) is absurdly low. And it remains true that nobody was spreading this idea up until the moment it became clear that the supposed Russian sock puppets appeared to be supporting both sides in the election. I remember it quite clearly. The supposed Russian master plan changed overnight after that.