"He reports to Wells Fargo that PayPal has engaged in fraud by taking these payments to fund his PayPal account, which is a false claim"

No, he didn't. In his own words:

"I told the representative there that I had reported the claim through PayPal, but wanted it noted that the charges made on my account that day were fraudulent in nature. The representative appeared to understand, and helped me make record of the incident."

The problem isn't with PayPal or his bank, as they'd eventually sort out the ping-pong notifications. The real problem is with Apple's draconian policy of taking all of a customer's purchases and data away from him if fraud reports occur on three or more occasions, regardless of why they occur (such as in this case with ping-ponging notifications between Wells Fargo and PayPal).

It's yet another reason to not trust your life to the cloud, and always procure a separate, pirated copy of your purchased software so that nobody can take it away from you.