I think Landy nailed it. The advantage to using a third party is that if somebody at the third party steals the money, that vendor will have bonds, insurance etc that will pay you what they owe you. (And then they send a guy named Louie with a baseball bat to get from the guy who took it).
Speaking as an accountant, I can tell you this is NOT how you launder money. Kim and Mickey may not be able to find out who ones that website, I can guarantee the courts and IRS can if they want to. Using credit cards leaves a clear audit trail. If they wanted to hide the money, they'd tell everybody to donate in cash and once a week a plane full of money who take it out of the country. This is a move in the opposite direction from laundering money.