Just like any existing matter, all the components of a printer cartridge may wear off in time, that is why there's a certain limit to which a piece of cartridge can be recycled. It depends on the condition of the cartridge itself whether how many times it can be reused, more likely 3 times is the minimum. I wonder how the manufacturers know the approximate number of times a cartridge has been recycled, perhaps there's a mark.
If you think refilling your own cartridges is considered a recycling process as well, in a way yes it is. But the real recycling process doesn't only involve refilling the tanks, it goes a long way. Refilling the cartridge by yourself has a higher tendency of getting a defective one. Also, if you inject enough ink into the tank then it failed to work properly, in the end you only waste the ink, your money, as well as the cartridge which might be more useful if you let someone knowledgeable do it. Unlike if you sent it to your respective retailer which has a cartridge return program, that cartridge you've wasted might have found a new life.
Cartridge recycling or any form of recycling stretches the useful life of a certain product, as well as the materials and components that it comprises. Although the print quality may not be as good as with OEM cartridges, the cut in price plus the environmental benefits that it provide are good trade-off. In addition, cost is not the primary factor to consider when determining the best quality. Remember that what matter is how you print, not by how much have you spent for it.