“The gra was fed cnn style news about the Alter Rebbe: he was told how the head of the “Katt” was seen eating on Tisha bav with his chassidim with a female on his lap. His informers conveniently forgot to mention that Tisha bav the year of the incident had fallen out on Shabbos, so it was nidche, and the female was his 3 year old granddaughter…”
I know that is what they say and it is quoted in Sefer Bais Rebbi, however do you really think the entire Cherem was only based on that so-called fact? Do you think that was the ultimate factor.
Even according to the above mentioned בית רבי there was the issue with Chasidus of Kalisk, who even Chabad considered them as Apikorsim , which was another factor. (It is mentioned that there was a debate in the town of Shklov, and they lost the debate due to the above chasidim – they were extremists – similar to nowadays Meshichists’)
In fact, the ones familiar with the shitas Talmidie haGRA have a total different story, they say the hisnagdus was not what people think it is. It went way beyond that and, it is really based on the core of Kaballistic yesodos in Emunah .