My opinion only, but I don't think that the Botkins were involved with a scam. I would imagine their grief at losing their father ran very deep. To think that perhaps one of the grand duchesses survived may have made his death seem less senseless than it really was. So, I believe their grief caused them to be mistaken about AA.
I'm a bit confused about the Kolya seeing Sednev in the Ipatiev House statement. There were two Sednevs. Ivan Sednev was the grand duchess' footman, and he was removed from the house with Nagorny, and like him was murdered. Ivan's nephew, Leshka, was removed from the Ipatiev House only hours before the murders. He left Ekaterinburg fairly soon after that, because I don't think he saw Kolya again, but I may be mistaken.
As to Leshka, he died, allegedly of typhus, in 1928, so he was very young when he died. I have always thought that Stalin had him murdered, but this is my opinion. To my knowledge, he left neither a statement nor descendants.