This just started happening a week ago. I've been using this printer for a few years! Phaser 8560MFP - home office environment.
Example: Type a word doc, click on FILE, SAVE. As soon as the dialog box for saving the file opens - the printer wakes up. This works for almost any dialog box that has to do with files (example: open, save, explore, save as).
Running Windows 7.
maybe there is some snmp communication
open up the driver properties, in one of the last tabs there are bidirectional settings, disable those :)
also in the port tab, click on configure port and disable snmp if it was on :)
maybe that helps?
maybe you can disable those communications ports also on the machie itself? did you have a look on the webinterface if you can disable those protocol ports?