I've been thinking about how we can make the statements made by obi-wan work in Ep III. I think that having a clone of Anakin taken from his severed arm would work to make those statements work. obi-wan could have witnessed this and thought that this dobbleganger killed the real anakin and thus fought him instead of anakin. That would be why he said vader was a pupil pf mine until he turned to evil. But the twist would be that the real anakin killed the clone, because he was the darker of the two.
You could also play sidious and tyranus' exchange at the end of ATOC in light of this info. Tyranus could have had anakin's severed hand taken on-board his ship before he left.