V70R AWD with automatic towed away

Yesterday my new V70R AWD with Automatic transmission was towed away the same day I had picked it up. Apparently the towing company saw a new car on my spot, didn't look for the parking tag in front of the windshield, although it was sitting right there, and towed it away. Then as soon as they found out it had the tag sitting there, they towed it back again to the lot!! (You'll understand this was not the smartest tow truck driver on earth.)

So when I called them this morning to ask why it was towed and where it was, all that the towing company had to say to me was "We brought it back to the lot at the front of the building- okay?" When I said that was NOT "okay", they hung up. I called again as friendly as my patience would allow me, to ask if they had considered the AWD system. The lady told me that their company tows everything, 2WD, 4WD and AWD, and she hung up again! No chance to ask if it was a flatbed, whether they had 4 wheels up or only two. I'm gonna talk to the towing truck driver tonight to ask how he towed it.

Bottom line, I'm worried that my car is messed up for which they're gonna have to pay. If they towed it 2 wheels down, how do I find out that anything of the transmission (incl automatic gearbox, Haldex system, differential, tyres, engine) is damaged?? Any mechanic out there who knows the answer? It seemed to drive okay this morning and no warning lights or messages popped up.