I agree that, assuming the limits of the resistor tolerance, you proved that the end series equivalent resistor tolerance will definitely be within the same tolerance. However, you didn't note that you'll statistically improve tolerance by using a bunch of resistors in series. I'm not sure that there's anywhere that it's practically applicable, but imagine that I have 1 million 1ohm 1% resistors, and one 5% 1Mohm resistor. It's certainly possible that the 5% resistor will be spot on, but given that you've effectively averaged a million 1% resistors which are, on average, perfectly spot on accurate, the chain has better tolerance!

Of course, a million 1ohm resistors is a bad example, since contact/joint/lead resistance will begin to dominate the error.