You can absolutely get precious metal from electronic waste. The issue with this story is that the amount you would get off of a SIM card would be significantly less than the cost of a postage stamp for someone to mail it in.

If they magically stumbled on a giant bin of SIM cards, sure it would be worth it. But people go through so few of them that no one has a drawer of them sitting around waiting to be recycled like batteries or plastic bags.