What constitutes a transmission line?
Would the leads of the resistor (although very short) not make up a sort of transmission line with its own characteristic impedance?


The leads of the resistor will (mainly) introduce parasitic inductance. This will make the resistor not behave exactly like a resistor, but like an LR series combination. 

Of course this means that when the inductive term becomes significant, the termination will no longer be matched to the characteristic impedance of the transmission line, and you will get reflections.

If you increase the frequency further (to try to make these leads look like transmission lines) you'll probably get into a regime where you must do a full electromagnetic analysis (to find how much they radiate, like little antennas) before they ever act like transmission lines.


  Why would there be no reflections?


There's no reflection when you terminate a transmission line with a matched load because the ratio of I to V in the load is equal to the ratio of I to V in the forward travelling wave on the transmission line. Therefore, there's no impedance mismatch at the connection of the line to the load.

Looked at more mathematically, you can say the solution to the boundary value problem for the transmission line with a matched load is to have no reflection.