I will follow the advice about printing some garbage and clearing the spooler
That seems like a waste of toner. If you're using a Linux LIVE CD (offline!), everything runs from RAM. Turning off your computer is enough to lose everything on your LIVE session, and turning off your printer does the same on the printer.
I thought that some modern printers actually had a sort of hard disk inside that stores many images of scans or prints, even if you clear the PC printing spooler ?
According to
Do All Printers Have a Hard Drive? it's much more common than I thought, I expected only the very big printers (like
this one) to have internal storage capacity.
If a printer stores the last prints, I would assume a printer can re-print the last page even after it has been turned off. My printer even starts processing data from the computer again when it has to print the same page a few times, so I'm pretty sure it doesn't store anything.