Over the years I've seen threads like this go dozens of pages and it's always the same old story. The word "could" gets thrown around endlessly.... Hell, a cow COULD fall through my ceiling and kill me before I finish typing this post.
Yes, your insurance company COULD deny you but no one ever can produce a concrete incident of this happening. Once you're in court anything is possible but in general your insurance must/will cover you unless you're committing a serious crime (overloaded as a consumer or speeding don't come close to meeting that bar). The insurance company would generally have to prove you set out to defraud them (staging an accident, etc.) or you'd have to be willfully committing a felony.... like a high-speed chase, etc. Joe six-pack being an idiot and towing a few cases of beer over his limits en route to the campsite isn't even close to being denied by insurance. The whole concept of insurance is to protect you when you do something dumb.
Far more likely than insurance denying you is, if you have assets, getting sued above your policy limits. I used to serve court papers and saw this all the time. Basically, if you have a pot to pee in you'd better be sure to have A LOT of insurance.
