Towing an AWD vehicle with one or both axles rolling, without being in neutral, could cause significant damage depending on how the vehicle is designed. Some vehicles are very sensitive and damage can occur even if the tire tread depth is different between tires by more than two or three 32nds.

Damage can occur to the engine, transmission, differential, and/or power transfer unit. The issue is that those parts will be accelerated to a high rpm unintentionally, and that can cause damage when there are computer (or human) controlled valves or other parts that would normally be opened or closed during operation but since the vehicle is being towed, those parts are in the wrong position. If it is a manual tranmsission, clutch and flywheel damage can also occur.

The most common damage I have seen from roll towing an AWD car is a cracked/broken power transfer unit case and cracked/broken transmission case. I have also seen twised driveshaft tubes, burned automatic transmission clutches/steels, and a differential pinion that became powder.

If you're questioning the safety or condition of the vehicle, take it to a professional to get it inspected.

Depends heavily on the AWD system.

Subaru full-time AWD will basically blow up in half a mile if towed on two wheels. I have no clue how Nissan's work, so it may range from "disconnected while off and its OK" to "car is totalled"

If he thinks something is off, get a mechanic to inspect and write an official report, and if they fucked it up, get a lawyer and expect a long ugly battle. Tow companies are scummy fucking shitbags and will use every trick in the book (including unenforceable, illegal disclaimers and contract terms) to get out of having to pay for the car.

The manual doesn't recommend 2-wheel towing awd models without using a dolly. ~~It's not aggressively against it which makes me think it might not be an issue for short/slow tows.~~ edit: actually the nice blurb is followed by a warning saying never tow an awd with wheels on the ground.

The system generally runs in 2wd mode but it's not clear to me when exactly the rear wheels engage. I beleive they are engaged when first accelerating, but it doesn't say anything when the car is off.

It's possible something is damaged, but it's less likely than just being hyperalert to an existing noise. A Nissan shop or at least a Nissan forum would be a better source for this exact condition though. I didn't see it wasn't in neutral, that makes no sense from the towing company's perspective. You should make sure "park" still stops the car from rolling.