How do insurers apportion responsibility when airliners collide on runways or taxiways?
Insurance is a contract between the airline and the insurance company. Typically, the airline is simply compensated an amount by the insurance company and the case is closed.

Demand to another party for settling damages only occur if the damages is unusually large and one party is mostly at fault. You have to consider the time and cost taken into legal proceedings as well.

Insurance compensation actually occur more frequently than you think. For example, at my airline, someone either forgot to apply the brakes on the food trolley or the brakes failed. Either way the trolley smashed into something during ground operations, resulting in damage to the trolley itself (I heard it was destroyed). Insurance paid us.

Regarding the specific incident about airplane collisions on taxiways, it is highly unusual. My guess would be it was handled as a "special case" in this instance.

You are correct that any investigations, if any, focus on preventing future occurrences rather than assigning blame. Settling damages is a civil matter; as such insurance companies rarely launch their own "investigations". Even if they do, it would just be a corporate and expensive version of two drivers using dash cams to argue who has to pay for the stretched bumper.

At any rate, insurance may compensate the airline even if employees of the airline are at fault. That is what insurance is for.