At the bottom of the waste tray well is a sensor which detects the presence of the waste tray. This sensor was stuck. Wiggling it with a long ruler solved the problem.
My 8560 DN asked me to empty the waste tray, which I did.
It just keeeps asking. I did everything I could imagine, shut down, unplug even, nothing doing, it just keeps on with the request to empty the waste tray