He never lied in that video.
your joking right??? How about the most obvious one "Your father wanted you to have this, it's his light saber"
Anakin and Obi Wan never have a conversation about that. So how could Obi Wan know he wanted him to have it? Anakin didn't even know he was going to have a son.
Now if Obi wan said "Your father WOULD HAVE wanted you to have this' then you would be correct.
Obi Wan also didn't take it upon himself to train Anakin when they met. He tried to convince Qui Gon NOT to train him. It was Qui Gons dying request that Obi Wan train him and even then he did so reluctantly