From what we are giving, I can see where Owen would have said something about Anakin running off and getting himself killed. Obi-wan turns it into what he said. He knows that if Anakin had died instead of turning, that he would have wanted his son to have his light saber. They were together for many years after all, first as student and master and then as friends and comrades in arms. And Obi-wan never owned R2 (he had an R4 with an R2 head and you can debate weather he owned it or whether it was just assigned to him).

The biggest lie is where he tell Luke that Vader killed his father. It might be just coincidence or that George had an idea that there was more to the story that Ben wasn’t going to tell luke, but Alec gives this wonderful face which in retrospect shows that you can’t really believe what he was about to say. It was a mix of truth and lies aimed to get Luke to start his training. The dialog in ANH reveals just how little Luke knew of his father and how much he wanted to know. By putting it the way he did he ensured that Luke would take the lightsaber.

Ben, like Threepio, is not very truthful in ANH. And you don’t need the prequels to show that.

So when you get to the prequels, nothing in their OT dialog really ties them to what happened in the past with any certainty so I don’t see where it creates any issues at all. The events of the PT are two to three decades in the past and memories can get fuzzy. Even for a Jedi. Leia remembering her mother is probably the biggest sticking point. I think Leia being psychic through the force is the best way to explain it. She is not the same as Luke and doesn’t have the same abilities. But even Vader noticed how strong willed she is and was surprised that the torture didn’t work.

I’ve found the best way while watching the movies is to just take it as it comes and don’t assume anything you hear is the truth. And just don’t think about it too much.