Suddenly you are lying by the side of the road, dazed, dusty, and injured. You know that you are not dead, but you also know that things are not good: the car is a twisted mess and your head hurts like hell. What is your first thought when you "come to"? No problem, I will turn it over to my insurance carrier. What is your second thought? Gosh, maybe I should have told them about my prior DUI when I filled out the insurance papers.
You do not want this to be you - whether in dealing with auto insurance or with athletes' insurance. All policies that I have seen have an application to fill out. The application asks you for prior lawsuits or criminal history and prior matters that could give rise to a claim. At the end of the policy application, there is always a note that the application becomes part of the insurance policy and that failure to level with the insurer will void coverage. So, what does this mean? Treat it like a meeting with your doctor - tell them everything. Better to get it out in the open, then to worry about coverage being negative when you need it most.
Yes, juries may not be crazy about insurance companies, but judges generally do not have that attitude and if they do, they bury it. However, judges routinely throw out cases where the policy application is false; in many states that falsehood does not even have to be material to get rid of coverage. As my 5th grade teacher used to say, "A word to the wise should be sufficient."