Ya I lost a lot of time because of this one, it's probably the best way to get public support early on. There is probably an offroad pickup truck parked near the mission marker in town, but any Offroad will do, and then there is a large brown box sitting on the ground somewhere in your HQ. You can buy an Offroad at your HQ for pretty cheap.

I think the text script might have being outdated. Usually a city supply mission generates a brown cardboard box next to petros which you can load on to an offroad or flatbed. You have to park the vehicle close and sometimes it is quite buggy so you cant load it on to vehicle.