What is the 'correct way' for AAA to tow a prius that does NOT run?

working 12 volt battery, neutral, flatbed.

can't make the car ready, wheel rollers, flatbed

 

Front wheels (at least) OFF the ground.
There are various ways to accomplish that, depending on whether or not the tow truck has easy access to the front.

 

Make them put it on a flat bed.

 

Fugedabout Neutral. Nobody tows with the front wheels on the ground; that's just asking for trouble.

You basically need to ensure the wheels that are on the ground can freely turn, so:

If they can open the car, release the parking brake, and the rear wheels are not seized for whatever reason, then they could tow with the front raised, rear wheels on the ground.

If they can't open the car, and the parking brake has been set, same as above but rear wheels on dollies.

This stuff is not hard, just need to think it through.

Any tow truck operator will (or dang well should) understand this; they do it every day.

 

Have you checked the owners manual? It tell you what to do. There is even a tow eyelet in the spare tire area you screw into the front bumper to pull the car onto a flatbed with.