That doesn't quite sound right. Typically body shops are fairly close in their labor costs.
Now, if the Tesla approved body shop is higher than all the other body shops for labor, then I would take that up with the body shop and tell them to work with you on it. Here is a Q&A at the body shop that I used here in the Dallas metroplex with regards to insurance companies. Seems to be a common occurrence:
Choosing a repair shop other than one the insurance company recommends
The insurance company representative may suggest several body shops that will perform the repair immediately, tell you that the insurance company will not guarantee the work done by the body shop you have chosen because it is not one of their preferred shops. Do not be concerned about these statements, every reputable body shop provides a lifetime guarantee on their work. Any insurance company guarantees or warranty work will be performed by the repair shop that did the work in the first place. Starting the work immediately will not likely change the date your vehicle will be ready for you and the scheduling of the repair is up to the body shop doing the repair.
The insurance company representative may tell you that the body shop you have chosen charges more than the going rate and you will have to pay the excess. Work is done only with your consent. Any differences in labor rates are handled before the work is started. In any event, the insurance company is required by law to pay reasonable repair costs. In a market with as much competition for your business as the Metroplex, no business would survive if the rates they charged were not reasonable. We will help you with the insurance company if they refuse to pay reasonable rates.
The insurance company representative may tell you that an adjuster cannot be dispatched for several days to the repair shop you have chosen, but if you go to one of the preferred shops the estimate they provide will allow them to start on your vehicle’s repair right away. You have the right to prompt processing and payment of claims after reporting the claim under Texas law. There should be no significant difference in the time required to repair your vehicle if you use the body shop of your choice.
They are trying to steer you to one of their gauranteed shops, but its your choice on who fixed your car. And from being in your shoes, I don't blame you for wanting a Tesla authorized shop working on my Model S. The body shop I went to walked me through his entire shop, and I got to see the behind the scenes action. There were notices all over the place in reference to certain standards that Tesla encourages, especially in the painting room where the paint is baked on (can be delicate with the batteries, electronics, etc.)
So I would talk with your body shop and tell them what the insurance company is telling you. I'm willing to bet they will help you out.