I think it’s perfectly plausible that George Michael who knew he was leaving Wham and his friend behind - a friend with very little talent who would never amount to anything music wise-gave Ridgeley the writing credit so he would be set for life. Everyone knew it was going to be a huge song.
George Michael was a very generous person. Countless examples of him helping people ….strangers! (most anonymously….many have come to light). Why wouldn’t he help his best friend that had helped Michael as a kid dealing with coming to grips with his sexuality and accompanied him every step of the way to and through stardom?
If you read about the song Ridgeley doesn’t appear to even be present when Michael comes to the US to try to record it with Wexler at Muscle Shoals. It’s Michael making every single decision… for example about the (in)famous saxophone bit..having sax player after sax player tackle it until finally one gets it in a new attempt to get it right in London without Wexler. I believe Michael plays virtually everything in it and Ridgeley doesn’t appear on it.