This is only half true. An inventory is done on an impounded vehicle, however, am inventory cannot be done for the purpose of finding evidence of a crime. As the police suspect the car is full of stolen goods, they will need a warrant to conduct a search of the vehicle or risk having all the evidence they find tossed out by the court.When someone is arrested and car impounded, a warrant isn't needed, what they do is an "Inventory" of the impounded vehicle so that when the owner gets it back he can't say "hey, my laptop is missing". This is common for any impounded vehicle. I don't know what the police told you but they do inventory impounded vehicles.
Also be sure to tell them you left your windows wide open and your keys in your cup holder in a junky filled neighborhood so at least the guy responsible catches a little bit of a break.