I think that the Musgroves have adopted the comforting idea that LR talked Anne out of marrying Charles. It is certainly easier to blame an outsider in their circle, rather than Anne herself, who they all like so well. Perhaps, they knew that Anne consulted with Lady Russell on the decision, so assumed that LR was against it, even though they got it backwards.

After that, it would be easy for adoring sisters to imagine that the woman that could persuade someone from marrying their eligible and beloved brother could persuade anyone to anything.