I guess that running power in a circle like that as fast as possible might heat up the battery, which reduces internal resistance, which increases battery voltage during load, which tricks the sensor that uses voltage to estimate charge.

It similar to when a fully charged but very cold car battery cannot start a car, as if the battery was discharged. Then you turn on the cars lights for a while, which to the cold batter is a significant load. The battery heats up, and then you can start the car.