That gave me a flashback to this Get Behind Me Satan era message:source
I thought of this too, but I think a lot of Jack's anger toward Chris Handyside stemmed from Handyside's review of Get Behind Me Satan and suggestion that Jack's marriage was a farce. Chris Handyside actually did get input from The White Stripes' close friends and associates when he wrote Fell In Love With a Band.
Here is Chris Handyside's review of Get Behind Me Satan.
Sounds like there was some bad blood there.