Nothing he does right now is as important as what he did. Nothing he says is believable. He had said earlier that he did not take Leiby into the wedding but left him in the parking lot. All of a sudden his story changed? He was seen on the wedding video without Leiby, so did he just let him walk around the hall by himself? Would he have taken that chance? But no one at the wedding saw him there. At this point in time someone would have come forward and said they saw him at the wedding.
He said he was surprised that Leiby was still in his apartment when he got home from work so he made him a sandwich, etc. But now we know that he drugged him and tied him up. Let him keep talking so he digs his own grave.