Hi, I live outside the US, and I ordered cake stuff from one of the well-known websites, (which I prefer not to name). The Billing Address was my husband's, but the shipping address was in the US, where my sister in-law lives. She's coming to visit us in 2 weeks, and she will bring my stuff with her.
After placing the order and paying by Visa, I received an approval on the transaction on my email. The next day, I'm surprised by an email sent to me by the website's customer service, telling me that I have to send them a copy of the front AND the back of my signed credit card + a copy of the electricity ill + the shipping and the billing adresses should be the same!!
I told them that this was impossible, no one would send their credit card that way, but I told them that I can get them anything else they needed to prove that the credit card is mine, and not stolen, but they insisted that the copy of the card was THE ONLY SOLUTION, otherwise they will cancel my order.
My sister-in-law tried talking to them, but they insisted on their request.
Needless to say, I ended up canceling my order.

Has anyone faced such a thing??

That is strange because there are a lot of websites when you order that allow you to have a different billing and shipping. What if you were sending it as a gift??? I have never encountered such a thing. Have you contacted the Better Business Bureau (BBB) to check out the business? They may be able to give you some advice. I would not copy my credit card though and send it to them. That is not safe.

I have been through that with Dell computers. I ordered a new computer, inside the U.S., but I was going to be away for surgery in another state, so I had the computer sent to my parents address.

Every time I tried to get help with the customers service, they wouldn't help me because the ship address and my address were different, and the name on the pacakge was my Mom's and not mine. I will never order from them again. Not just because of that, but because of their customer service.