The issue here is voltage drop in the circuit supplying the saw. The saw's motor has an optimal voltage range, and will not run well if the voltage is too low. The voltage drops over the length of the extension cord; the longer the cord, the greater the drop. However, a heavier gauge cord will have less voltage drop than a lighter gauge cord.
(Voltage drop is a factor right at the receptacle, even without an extension cord - the gauge and length of the wiring from the panel to the receptacle, the load on that branch circuit, the load on your whole service, the gauge and length of your service conductors / feeders, heck even the load on neighbors service can affect your voltage at the receptacle.)
You didn't mention the manufacturer specifying a gauge for the 50' max extension cord, let's assume they figure you'll use a 14 gauge cord, and let's assume the saw draws a full 15A (which it probably does not). The voltage drop for that 14 gauge cord at 15 amps is about 3.79 volts. A 12 gauge cord 100' long at 15A will drop about 4.75 volts. So I'd feel completely confident with a 12 gauge 100' cord - one volt is negligible.
If you really want to test the voltage drop, testing at the end of the cord doesn't tell you anything because you need to see what the voltage is under load. If you really want to test this, and if you can do this safely, you could plug a receptacle splitter or power tap (rated for the load, of course) and check voltage while someone runs the saw full bore cutting wood.