What I haven't seen anybody mention so far is the possibility that Skyler could have just refunded/sold the necklace. It's what I would do if I had an expensive piece of jewelry that wasn't very dear to me. It sucks to think about, but the guy is clearly a prick and I wouldn't be at all surprised.

And even if he hasn't done that, he could just lie about it. The obvious response to being called out this way would be "I sold it, lol".