There is really no such thing as "full coverage." When most people use this term they are referring to physical damage coverage which usually includes collision and comprehensive coverage. Typically, comprehensive insurance covers damage to your automobile from vandalism & theft (among other things) while Collision covers damage to your automobile cause by a collision with an object or by upset.

That being said if your boyfriend's insurance policy does include collision and comprehensive than his car's damages should be covered. It sounds like there is confusion between what your boyfriend believes to have on his insurance policy and what the insurance company is saying that he has. Your boyfriend needs to read over his insurance policy and then speak to his insurance company or agent again about what actual coverages are on the policy.

You can learn more about coverages and definitions here. And you can shop for an insurance policy by getting a car insurance quote here.