Odd one, as he did own up when quizzed, although why wear it if it isn't yours to wear? Has dad passed on, perchance? Only wonder as I'd expect he wouldn't be too chuffed with the wearing of said item if he is still very much around.
We were at a wedding once when a bloke rocked up wearing a winged dagger tie, one of the lads with us was one of them and went up to chat to him, turned out the bloke sold ties and said if he sold them he could wear them!! He went home tieless!
When I was a kid and needed a tie one day, my dad wouldn't give me his cos it was a Regi one. Nicked one for me off his mate though.
As to your mate, if he's wearing it at a location that no-one will notice and he doesn't mention what it is, fair enough. If either of the above apply, then no-go. So, he's a walt if he wears it again. Just my opinion.