I do not blame the business owner who is a bit nervous about having all of her data in remote servers. Of course, I do think this is the way to go and your data is 99.999% safe. However, having your data on premise might be comforting as well and maybe there are clear legitimate reasons why you want to have on premise access to your data as well.
Some companies are using a dual approach – having their data in the cloud (hosted online) but also readily available on premise. Egnyte has been pushing this kind of solution for some time now and they have an updated solution, Egnyte HybridCloud.
Hybrid cloud solutions (Egnyte’s or others) have your data in a service providers data center but then also use an on-premise storage solution that is synchronized to the online system. You now can access your data from the on-premise solution or when traveling or in case something happens to your office you also have it safely backed up online.