I don't think the ink monitoring becomes inaccurate because the chip is damaged or changed by the resetter.
Instead I think the reason is loss of sponge capacity.
New OEM CLI-x21 cartridges have a nominal capacity of 10 ml. Nominal capacity means the ink amount used in production of the cartridge, not all of the ink can be used, 1-1.5 ml is left in the sponge when the cartridge is declared empty by the printer. This is to protect the print head, as a steady supply of ink is vital to cool the nozzle heaters, else they risk burning out.
The ink compartment of these cartridges has a capacity of around 3 ml IIRC. The rest of the ink is in the sponge. When the ink compartment becomes empty the prism triggers a count down based on number of nozzle firings and cleanings. The low ink warning is not issued yet as there still is around two thirds of the ink amount left in the sponges. When the printer
estimates the ink is running low a low ink warning is issued. When the printer
estimates the cartridge is near the end of the cartridge's useful ink amount an out of ink warning is issued, and printing is halted. You can override this warning, but this is not recommended.
The ink level displayed is not based on measurements, it is a calculated value, based on the number of nozzle firings and nozzle cleanings, If the sponge in a refilled cartridge contains less ink than the sponge in a new OEM cartridge, the ink out warnings will come too late, and the print head is at risk, as the count down is based on the ink amounts in a new OEM cartridge.
Therefore it is a very good idea to refill the cartridge when you get the low ink warning, as stated by The Hat. Waiting for the out of ink warning is risky, the cartridge could be out of ink before the warning is issued.
The condition of the cartridges/quality control of your refill can be done by weighing, The weight of a new OEM CLI-x21 cartridge without the orange seal and vent sealing tape is around 20.3 g. If the refilled cartridge is more than one gram underweight the cartridge should be flushed and dried before a new refill. The pigment PGI-x20 has a nominal capacity of 19 ml and the weight of a new OEM cartridge without the sealing clip and the vent sealing tape is around 35.3 g. If a refilled cartridge is more than 2 g underweight it should be flushed and dried before a new refill.
These weights also apply to the opaque PGI-x25/CLI-x26 cartridges. Except for being opaque and having a different chip they are identical to the windowed PGI-x20/CLI-x21.
The most probable cause of this loss of capacity is that running the cartridges too dry causes air to be sucked into the sponge. This air is not always replaced by ink when refilling. Refilling early at the low ink warning greatly reduces the risk of capacity loss.
Much more about the sponges and their role in the proper function of the cartridges can be found in the thread
"FLUSHING....WHY?". This (lengthy) thread contains a wealth of information if you want to understand the Canon cartridges which at first glimpse appear to be nothing more than simple ink tanks. It is certainly worth reading IMO.
If you paid for having your cartridge refilled, you will of course try to squeeze every drop of ink out of the cartridge, but doing this with a refilled cartridge is risky. Maybe this is the cause of the problems with the MX860?