What are the current sense resistors for in the "typical application" on the LTC4370 datasheet
You've misunderstood how the circuit works. It doesn't care about absolute voltage to the load. You have to keep in mind that the two sense resistors are tied together at the load, so the voltage into the the chip differs only according to the currents through the sense resistors. What the IC does is try to keep the two currents totaling some predetermined level. So if one supply hits its limit and can provide no more current, the voltage across the two resistors is adjusted by increasing the current through the other side, drawing more current from the other supply.