Technical basis for this tutorial comes from the Square-D company that makes circuit breakers used in their panels for industrial and residential uses. These are designed to the same guidelines of the National Electrical code as other manufacturers' breakers so the operation should be the same.
I think the typical person thinks circuit breakers are black and white devices. That is, for a 15A breaker that if the current is 14.9 amps it will continue to conduct and if the current rises to 15.1 Amps it will open up and disconnect the circuit.
But in reality, circuit breakers are both time and current sensitive. This is a very useful thing because it allows us to use devices which vary in current pull so that the average is 15 amps and have peaks (say when your saw encounters a knot, or when a motor or light bulb turns on) very much in excess of 15 amps.
If you look at the end of the reference document, it has trip-point curves for the breakers , time vs. normalized current (e.g. the rated, or handle current is considered to be "1"). The curves and the text say that the circuit breaker should conduct the rated "handle" current (e.g. the value marked on the handle) pretty much forever if the ambient temperature is less than 40°C (~104°F). If the current is over about 1.5 times the rated current for longer than 10-100 seconds the breaker will eventually trip.
The curves approach the rated current when the time exceeds 10-100 seconds, this is because one trip mechanism is a bimetal element that is heated by the current flow. The element takes time to heat up to the trip point, allowing brief overcurrent surges since the heating takes time. And, devices shifting quickly from 10-20 amps and back but averaging 15 will also work forever.
The other feature of the curve is that around 9-10 times the rated current (about 135 Amps in this 15A breaker example), the breaker trips within one AC cycle (a few milliseconds) due to the electromagnetic trip element based solely on current. This is sufficient to let motor and light bulb starting curges through.
Between the two portions of the curve, like from 1.5x to 9x the rated current, the time it takes to trip decreases from 10 seconds to less than .3 of a second.
Thus you see that circuit breakers will trip immediately on gross overcurrent levels starting around 9x the rating, but allow brief, surges in the 1-10 second or more range. this is consistent with motors which can stand brief surges without overheating due to the thermal mass of the motor.
If you understand how these work, the people who put a 20A breaker on their dedicated circuit for their BT3100/BT3000 are just fooling themselves and taking a risk that the saw will melt down when overloaded. A 15A breaker for the BT3100/BT3000 is more than sufficient, given the leeway designed into the breakers. A 15A breaker is more than sufficient, allowing current surges consistent with startup and brief surges in operation associated with knots and feeding inconsistencies and other short term irregularities which do not exceed 15A on average. It will also protect the 15A-rated motor properly since the saw itself does not use any current overload protection.