They are wrong in this case. Many private citizens can take credit cards through various apps, websites, and even some banks. If you wanted to pay me right now via cc I could set something up in about 3 minutes.
As I said, I paid via CC multiple times to different sites, and in one case a private person. Not all may do this but I have only ever used CC and to say none do, as the other person did, is wrong.
I'm saying some do, not all. He is dealing in an absolute that is simply false. I'm not trying to be harsh but spreading false information is not helpful to anyone involved. I apologize if you're not familiar with the various ways/apps that allow for taking credit cards now. They're out there.
I would NEVER EVER use paypal. My CC offers 100% protection vs scams or failure to meet the agreement, paypal has a long and stupid dispute process.
To be clear here, if you don't know the answer but yet decide to insist no dvc rental places/people take credit card, that's making stuff up. That's it. If you don't know the answer, the best action is usually to either offer what you do know with a caveat, or what you think with a caveat, or say nothing at all.
I don't know all take CC, but I sure do know lots do. CC is safer for the seller and purchaser. It is relatively easy to defraud paypal from either side. Have fun trying to pull that off with a CC.