Isn't it funny I just called Nationwide insurance Company, and you can get insurance on your home or car over the phone in about 3 min.
Nationwide is a for profit corporation with REALLY deep pockets. When you have money you can bend some of the rules. Did you ask Nationwide if you don't have to agree to their terms if you want their insurance. I bet a buck they will send you something that you will need to sign and return within a certain time period.
I can assure you if insurance was not part of the deal, then they would take the info over the phone, however they have liability. Once you agree to terms, in some physical way, the liability is then transferred from them to you. This way when you go to sue the AMA for something you weren't covered for, you can't say "they never told me about that". Obviously, some of the members of our "club" don't hold a full deck of cards.