Some credit cards allow you to chose your own picture to be printed on your CC.
Credit card fraud just happened to us. Just got back from Negril and went to local grocery store. That's the only place the card was used. Never took it to Jamaica.
I take your point however it doesn't have anything to do with fraud or my comfort level with carrying a lot of cash, you're talking merchant fees.
To which I say, feel free to accept cash or checks only if that works better for your business. I know many that operate that way, my own business included.