David,
The risk or liability a detailing business owner takes on when they do business with a dealership is about the damage or loss of vehicle from the time it is delivered back to the dealership, prior to pickup by the retail customer.
Let's use the following example. A detailer picks up the vehicle from the dealership, takes it back to the shop, cleans it and returns it to the dealership without incurring any damage. The next day, the detailing business owner gets a call from the dealership, explaining that the car is damaged, with a large dent in the rear quarter panel. The detailer knows that this had to happen after the vehicle was returned to the dealership and it is clearly the dealerships responsibility. Rather than arguing about who is at fault and responsibile for the damage, the business owner simply has the option to contact their own insurance company and suppy them with the name and contact information of the dealership's garagekeepers insurance company.
In the above situation, the dealership may not have tried to blame the detailing business owner for the damage, knowing that the business owner had the recourse of contacting the dealerships insurance company. On the other side, when the dealership is holding all the cards and the business owner has no information, then the dealership can do whatever they want.
By asking for the dealership's insurance information upfront, you are simple leveling the playing field and making all things a bit more equal.