I don't think they are allowed to be moving while they have the gas and cooking equipment on. I'm sure there are many safety regulations regarding how they have to operate as far as being locked down before they can turn on gas, take out knives, etc. Plus, it's probably not practical or cost effective to use the truck to deliver stuff.
That being said, it seems they would be set up for just parking someplace and then delivering using other vehicles. But, I guess it's hard for them to pick a location where people would know they were or get people their contact info. Although I would think some of the more popular local trucks could probably do it through Twitter, etc.