Contrary to your suggestion, this isn't an issue of differing burdens of proof. This is a question of whether there is evidence to support a lawsuit.
The evidence of civil liability is slim to none. At a minimum, proof of liability means there is evidence of a negligent breach of some recognized duty under the law. A person is not negligent, and cannot be held liable for the destruction of a RC helicopter, just because he is operating a CB as he drives by the location where the RC helicopter is being operated. There must be something negligent about the operation of the CB that would make the destruction of the RC helicopter foreseeable. The idea of civil liability on these sparse facts is ludicrous on its face. In short, the helicopter owner may file a lawsuit, but there is no guarantee that he will win on those facts.
HOWEVER, if the state and/or federal courts take action first, and find the CB operator guilty of a crime, the RC helicopter owner wouldn't need any further proof. The prior criminal judgment in either a federal or state court works as a substitute for proof in a later civil action. I'm not saying this is likely. I'm saying that much stronger proof as reflected in a judgment would be required to make out this case.