It's not only for the gripper edge that printers leave a border around the
image. It would gunk up the printer's innards something fierce if the laser
toner or inkjet ink went beyond the paper's edge and onto the rollers.
You're absolutely right about going onto oversized stock.. The only other
way I can think of to get a "bleed" image would be to print the page, with
crop marks, as "fit to page" and make your peace with a reduced overall
image size.