Doing business offline gives you far more options to provide a range of customer service options.
As long as your policy covers you, covers genuine and sensible claims, and makes it quite clear that anything outside of those well defined borders will not be entertained, and explains why, then I think most customers will be happy to accept it.
A certain amount of flexibility where it is available always goes a long way as well, and is one of those great offline customer service options that you have available to you when the situation allows.
Offline or online, never going to keep everyone happy, but you can certainly provide a policy that is fair and suits most.