He never said he bought it during peak. He said he bought it around 10.
Not everybody checks their ticket so religiously. Especially if it was purchased in such an unusual way. I know if I buy a return I just get the ticket for that journey and put the other away in my wallet. It may have been a surprise to him that he didn't have the correct ticket on the way home. The video doesn't show the start of the conversation and the lad's ire may have been exacerbated by the conductor's attitude which may have resulted in him swearing at him and repeating that he had paid. Again we don't know either way. We can only continue to add more conjecture to the situation.
Perhaps we should have an online petition to see if the public give a fuck.