I have actually encountered similar situations in practice. What I have generally concluded is there is a financial motive. An accident occurs. Initially, the driver who was struck is either in a bit of a shock or in a hurry. They say they are ok and leave. After talking to people, they realize that they can file a bodily injury claim and "make some money." However, they don't have the insurance information. They file a false hit and run report and, as a result, obtain the information. They then proceed with a bodily injury claim.
That is always one reasonable guess as to why they do that. Also, there is always the possibility that the other driver is hiding some criminal activity that they do not want the police to see if they arrive on scene. These can include: possessing drugs or weapons in the car, not having a valid driver's license at the time or actually being under the influence of drugs that, while cannot be detected by regular individuals, can be detected by law enforcement who are trained in it.
These are all the types of questions that an attorney representing you will look into and ask of the other driver in Court. Depending on the answers, they can establish a financial motive, which in turn would diminish the other driver's credibility as to the events taking place .
About the policy limits in place, I can assume, based on your description, that would be enough coverage.
Again, you must understand that jail is technically a possibility, but it is not likely. Even with a prior DUI, I do not believe your husband would be sent to jail for this. As an example, some states classify speeding in excess of 25 MPH as a misdemeanor, therefore punishable by jail. In practice, no one gets sent to jail for speeding 25 over unless there are additional circumstances (i.e., accident leading to death, speeding 50 over, etc).