Yar, we have plenty of the flat beds like that and the type I would call if I needed it, but never seen a large crane and flatbed combo around here. I would guess that if a car was in a bayou in the US, it would be considered a total loss anyway (even a supercar, maybe) and yanked out of the water with chains and pullies.
As for how towing works here, it depends on the situation. If the police call for a tow on an accident where people are taken to the hospital or an abandoned car, it's often first come first gets the tow, but if the owner is there, they can request a certain company or tow truck type, if they want. The police will usually know that X car is too low/damaged and needs a flat bed.
It is also up to the owner to pay for towing separately, or at least I have never seen towing included in the insurance price.