I recently had this discussion with a restaurant owner that's been here for several years, and he informed me that before the digital slips, there were certain stores and restaurants that used to create carbon copies of credit cards, just like in department stores in the states back in the 80's and 90's. The problem with this was that employees had a perfect copy of your credit/debit card.
Unfortunately, in Belize, all that's required to make a purchase is the credit card number. I can attest to this, as I've extended golf cart rentals with just a credit card number. No name verification or CCV code was needed.
I've heard stories from several years ago of tourists being charged on their credit cards, and then with the carbon copies, dishonest employees making purchases and shipping to John Doe houses. I've heard allegations of ties with Customs to get the products imported and such, but then again, it could all be hearsay, right?
I hate to say it, but I think you got screwed by Billy's Store. The only time I use my card here is at ATM's or establishments where I have a personal relationship with the person that's swiping my card.
And another example of how loose security is here? I took a couple of visiting tourists to a very well-known restaurant here, and to prove a point (actually, two: that the bill would be placed in front of me automatically, and that I could pay with one of their credit cards without an ID; they were both female). Sure enough, the bill was placed in front of me. I gave them the credit card which was handed to me by Kathy earlier, and they swiped it and returned it without an ID or verification.
Credit card security is still very premature in Belize, and I wouldn't use it freely as I did in the States.