The endorsement makes the member an insured only with respect to his liability for the named insured's activities. In other words, the member is an insured only when he is liable for the activities he does for the named insured club. This makes the member an insured in case he injures someone or damages another's property while doing some work or project for the named insured.

So, in your situation, the member is not an insured when he got injured. He could not be liable to himself for being injured. The member suffered BI while on the named insured's premises caused by an accident. So, even if the member caused his own injuries by accident, he is entitled to med pay coverage. He is not an insured under the circumstances so there is no applicable exclusion to prevent med pay coverage, unless the member was hired to do some work for the named insured or if he was involved in some athletic activity.