It's not the resistors that have the inductance, but the tracks on the PCB. They have a "characteristic impedance" - the resistors couple with that to make a low-pass filter.
It's only a problem at incredibly high frequencies, which is why you see high frequency comms traces on PCBs with wiggles in them to keep the length, and hence the impedance, the same.
However, even relatively low digital frequencies have some very high analogue harmonics - so the normal effect is of a "rounding" of the nice clean square wave rather than a blocking of it completely. This can cause timing issues at high communication speeds, where one signal might not have completely risen to the right level before another (say a clock signal) has reached that required level, so the receiver gets spurious values.