It is good to hear that your insurance company is working with you to both pay out your claim and allow you to buy back your "totaled" vehicle. In most states the laws require the insurance company to apply for a salvage title before paying out the settlement.
If the new owner wants to drive the vehicle legally on the streets in many states you cannot do so with the salvage title unless it is "rebuildable". He or she can buy the car from you with the salvage title, repair the vehicle and get it inspected to make sure it is road worthy. Once this is done many states will then allow the title to be changed to say "rebuilt."
If the buyer of the vehicle is concerned about being able to insure the vehicle have them call their insurance company now to see what insurance they will be able to get. Or they can contact us at CarInsurance.com for help obtaining insurance.