I don't know that regen turns off. It's that a full battery has no capacity to take the current input from regeneration. That would be the case whether towing or not.
One thing I never got was that they could easily make the behavior consistent. Maybe regen isn't available when the battery is nearly full, but that doesn't mean that their only option is to let the car run away on coasting. Regen should have an option to simulate the resistive force when it isn't avilable due to SoC. Yes, it will use energy when your expectation might be to conserve energy - which is why it should be a choice for the driver/owner. But at least that could remove that sudden fright when you leave the house on a road-trip morning with a full battery and come to the first downhill. That only happens for me a couple of times a year as I normally am not at full when I leave my house on a daily trip.