I think the legal side of it could be a problem. Although I agree with the philosophy that people don't need to know unless asked, in this case you don't know what the terms of the insurance are. The worst case scenario is that a kid gets injured and insurance refuses to pay because the policy doesn't cover you if you have a known mental illness. Personally, that's not a risk I would be willing to take.

You could ask to see a copy of the policy to check what "outs" the insurance company has. I'm not sure if BSA has a legal person that you could call and ask, rather than having to ask the people you work with. As to whether you out yourself, or don't go that's completely your decision.

Good luck, and I hope it works out for you.