My understanding was that this was more of a stop sign than a brick wall trying to stop you from printing. I have not seen any examples of Brother enforcing replacements of parts in consumer products. Do you remember the model? There is one example of a multi-color laser printer where it complains about not having genuine toner, but there's a few links of firmware downgrades online if you know where to look.

My experience is that a, sometimes complicated, series of button presses for a specific amount of times resets the counter and it continues printing like usual. For the model I have the reset procedure is just holding the power button while turning it on for a specific number of seconds.