Regular medical insurance is pretty close to a "no fault" policy and generally covers all injuries, regardless of cause. Did they have a specific reason for only covering a small portion of your expenses (non-traditional treatment, out of country, too much massage therapy, etc)? If they did not give you a written explanation, it may be time to ask for one.
To actually answer your question, HPDE insurance only covers physical damages to your car. Your best bet for medical is to have your car insured with a company that does not yet have a track exclusion. That way you are covered just like any other accident.