I added the dining plan for some people renting my points. They had a Chase Disney Rewards card (actually 2) to use for it. They gave me the numbers, and there was no problem with it. I wouldn't be too comfortable taking a stranger's credit card information (I don't know if Disney would accept that from me, anyway), but I was fine with the Rewards card. In fact, they were able to use some Rewards that would otherwise have expired in December, because they do charge immediately, not 48 hours out.
The 2 cards were not quite enough to cover it, so they sent me the rest by Paypal, and I used my own Rewards card for the balance. The rep had no problem taking the three Rewards cards for payment. You could do the same with Disney gift cards: the person renting can buy a gift card with enough on it to cover the DP, and just give the member the number. But you have to plan ahead a bit with that, because you have to get the gift card at a
Disney Store or by mail. You can't use online gift cards -- those are only good at Disney.com.