I've been an attorney for over 10 years and I started out doing insurance defense work. People get sued for negligence in car accidents all the time. If you're towing an excessive amount of weight, that could be an issue that gets raised. It is unlikely to be the issue that determines whether you're liable or not, but it could conceivably impact the settlement your insurance company pays. I don't see a scenario where an insurance company would refuse coverage to an insured just for towing over a manufacturers weight rating, though - that would be a great way to get slapped with a bad faith claim.
The real takeaway from this little sidebar is you need to be sure you have adequate limits on your coverage.