I think what's going on is, there is a device in the motor circuit that measures the current flow throught the motor. If so, it's an adaptation of a device called a "slump meter" that was originally used in central concrete mixing plants (and still is). The principle is exactly the same.
Dry load: the load flows easily, so the drum is easy to turn. Less current draw.
Damp to moderately-wet load: the load is "stiff" so the drum becomes progressively harder to turn. More and more current draw.
Moderately- to very-wet load additional water lubricates the load so it flows more easily again: the drum becomes progressively easier to turn. Current draw goes down.
Yes, that's correct: it gets harder to turn as the water level increases up to a point, and from that point forward, further addition of water makes it easier to turn.
Also, a load that comes up to significantly below the center-line of the drum, will be harder to rotate than a load that comes up well above the center-line of the drum. The easiest rotation occurs with zero load and with 100% full load.
So my guess is, for a horizontal-drum washer, what the system is looking for is the point at which the water level is slightly beyond the key point at which the drum starts to become easier to turn.
Now also, if the washer measures the amount of water (for example via a flowmeter) that was needed to get to the point just past the "starts getting easier to turn" level, it will also know how much material is in the drum, which can be used to modify the cycle further.
Very clever. Simple & elegant.