Boy, did I get bad information from the scout leader and the coordinator.
I called GS house and they have insurance that will cover just this sort of thing. They offer to pay the first $100 of medical fees and then to cover our deductibles as a secondary insurance. The person at GS House told me that she sees no reason why this would be denied and she'll send me the paperwork.
I made it clear to her that if it will cost GS house more to have this covered, I don't want to pursue it further. I don't want anything more than to have the insurance help us out, if it is available.
She said, "No problem. This is exactly the type of thing that it is there to cover." She also said she'd have someone contact the leader to tell her what is available in the way of insurance if someone else needs to use it.