To get back to the OP's question.
Technically there is nothing preventing someone from doing what you have suggested, and I'm sure that it has happened, however, the accuser will have to provide a statement to the police about how, when, what, was stolen. So if the accuser gives you a gift and then claims you stole it but he doesn't know when, or how you got in the house, etc. You'll obviously claim it was a gift. There isn't going to be a lot of information to go forth with prosecution. I would guess that the DA, or police, would suggest you give the item back and leave it at that.
Another scenario is if the accuser files a report that you stole the item while he was at work (for example). You claim it was a gift and then show that you were at work and it is not possible that you could have stolen the item, then the police could look into false police report, etc as has been written about.
Basically, the details of the report have a small chance of holding up in court.