Prince played on the song. There's no debate there. Stevie and others who were in the studio attest to it. Yes, she has since worn the collaboration like a badge, and yes, she is prone to exaggeration, but that's beside the point. This was 1983 and she was at the top of her solo game and a huge figure in the public eye. There would have been no reason why this would not be believable.
The only surprising thing is her insistence on 50/50 publishing rights. Any number of her Mac songs have required more input from Lindsey and the rest of the band. It's like giving John McVie partial credit for his game-changing bass line in "Rhiannon." Because of him, a straight-ahead galloping rock tune became a slithering, seductive thing. Where's his royalty
On another note, the title of this thread is "New Book." I'm still waiting for the thread that will read: "New Album."