There's no "proof" of anything. That whole little write up was nothing but speculation, assumptions, and a little bit of fan fiction.

Unless you were in the studio, you don't know who was doing what and who laid the final tracks on the songs. Richie is still credited as a co-writer and co-producer. I don't believe Jon has any compelling reason to give Richie credit/payment/royalities for life for work he didn't actually do.