I hope this becomes a popular maxim - fed up of offline not working for productivity tools (not necessary for other types of apps, but Trello is a shining example of this omission making productivity apps near-useless).
But I agree that you could see the server as YAGNI, especially if all your app is doing is data consumption and your data is small enough to be downloaded to the device in its entirety.
I have written about caching and offline here: https://winch.io/blog/article/caching-prefetching-and-the-of... (warning: promotional content for a service that helps you do that for native mobile apps at the end).
As for local storage, even on smaller capacity devices, there's a whole lot that can be kept - why, for instance, does a todo list, addressbook, appointment manager, workout tracker, etc, etc, need to connect to a remote server for it's very basest of functions? Sure, backup, synchronization, sharing, etc need connectivity, but those aren't (IMHO, shouldn't be) the main focus of these apps.