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I've seen a good compromise approach in the iThoughts mind map tool:

Whenever you open a document from dropbox it downloads it and caches it - much like OmniGraffle or any of the Apple apps like Numbers.

However, it remembers where the doc came from and maintains a sync relationship with the source.

With a single sync operation it compares the versions (probably date based) of ALL the files you have in your cache and uploads/downloads the most recent as appropriate.

Thus after a sync the latest version of all the files you care about are replicated on the device and on remote storage.