We were both "sort of" right. Yes, half of Cheap Trick, (the "nerdy" half), guitarist Rick Nielsen and drummer Bun E. ("Cohn") Carlos worked in the studio with John during the sessions for Double Fantasy. Rick and Bun E. sat in during alternative versions of the songs I'm Losing You and I'm Moving On. Those songs were slated to be the versions for the record. Until...but later in the chapter, it was revealed why John nixed using those two versions of the songs. John felt the versions with Rick and Bun were "rougher sounding" than the other 10-12 songs slated to go on the record and that they would stand out as inconsistent with the overall vibe he was going for. They sounded also too much like Cold Turkey.
Cheap Trick then left for the rest of the tour they were on - to Japan. And using half of Cheap Trick was supposed to be top secret, (as was the entire session) but while in the studio John later picked up a copy of Rolling Stone magazine (9/18/80) and to his surprise, read a blurb stating (from Japan) that "Cheap Trick was recently at the Hit Factory in New York working on John Lennon's new album." That made him upset. It was also thought that Yoko thought those two guys were "using" John's fame, even though he has invited them. And, CT was pretty huge by then. In 1996/97 Yoko wanted to release a box set of John's music and the Cheap Trick versions are on that. The Cheap Trick is just a short chapter, the rest of the book is pretty good. Let me know if yo'd like to borrow it when I am finished.