The NHRA info on cooking in tents refers to the NJ State Fire Code regulating tents used for public occupancy, not camping tents for private use. Basically, the code requires a certification that the tent materials have a fire resistance meeting National Fire Protection Standards, a fire supprssion system (usually fire extinguishers rated "TYPE ABC" located in a visible location), adequate exits based on the anticipated number of people that will be in the tent, the posting of a "Maximum Occupancy Placard", and a temporary permit. As far as hospitality railers with a built in kitchen, this may have different requirements as far as a fire suppression system.
I strongly recommend that all teams using a hospitality tent/trailer, contact The Old Bridge Township Fire Prevention Bureau very soon to get their requirements so that everything is in place before you arrive for the event. Another source of info is the NJ Division of Fire Safety at the NJ.gov web site.
Our town hosted the PGA golf championship in 2005. There were many hospitality tents in use that had to meet these same requirements. It's not that hard to do if you have the info ahead of time. Just remember to give the local Fire prevention guys plenty of time before the race, and you should have no problems when you set up.