On the newer printers, you have to go through a procedure to fool the printer after re-fill to reset the timer. I don't remember the exact procedure. But the instruction for that is included in some of the re-fill (non-hpq) kits.
Like a lot of electronic tricks, the knowledgeable can get around it. The average home mom will believe the manufacturer's label and not take a chance. That Georgia woman must feel it personal.