In a four probe setup you are measuring voltage, not resistance. But you are right that the measurement can still influence the results when the voltages measured are tiny.

The way to think of this is simple: you can't measure anything without subtle joining the circuitry that you are measuring and that has an effect on the properties of the circuit as a whole for which you have to compensate. In this case: the voltage measurement is going to consume a tiny bit of power and that is due to the resistance of the measurement apparatus even if it isn't in the main current path but a secondary one. But the people that do these kinds of measurements tend to be well aware of this and will pick their measurement gear and reference current to minimize the chances of that happening.

I sort of don’t get this either. If your testing equipment is introducing resistance can you not “tare” or calibrate your measurements by measuring the equipments current flow in a direct circuit between probes to determine its base resistance then introduce your sample and measure the difference? The resistance in a serial circuit is additive, no?