Your car could also be towed... My brothers 91 cutlass supreme was towed from parking lot and it was hung by rear lower control arms which bent and cars alignment was lost plus bushings were very loose. Control arm were made of sheet metal un a shape of "U" . it wasnt hard to bend them .... so check your shafts, just lift the rear and have soeone spin your wheel..
you never know with those tow companies.
regards, Bart.