Just keep in mind that by leasing on to a carrier, you are transferring the right to possession and/or use of goods or equipment (your truck) for a term in return for consideration. The "term" isn't necessarily limited to only those times when you are under dispatch. The carrier can be liable for things you do when not under dispatch, even when you are OOS, therefore many carriers will have certain policies to limit their liability. You may be an independent contractor, but you are still leased with the carrier, which carries with it certain legal obligations whether you are loaded or not, namely, an implied Duty of Trust and Confidence, which is implied in all contracts, and basically means that neither party will, without reasonable and proper cause, conduct itself in a manner likely to destroy or seriously damage the relationship of confidence and trust between the contractor and carrier.
A Duty of Trust and Confidence is the provision that allows the carrier to protect itself with personal conveyance policies for a vehicle which displays their lettering and DOT number, whether that vehicle is in or out of service. It's what allows a carrier to prevent you from, say, parking your vehicle in a conspicuous parking space at the Nude Nude Nudie Girls XXX Galleria Day Spa Cafe. It's also the same provision that is supposed to prevent the carrier from likewise damaging the relationship of trust and confidence when penalizing you from turning down a load under a no-forced dispatch agreement.
So while the personal conveyance policies may seem arbitrary, even controlling, they are a part of what a carrier can do to limit their liability. If you cover up all lettering and are OOS with a Not-For-Hire sign on the truck (something you may need to get permission to do, or at least make them aware, depending on your contract), then a carrier is severely limited in what they can do to control your OOS time and movements.
