Actually, everything the app does is through a RESTful API. This API is private and undocumented (for now). I can't make any promises as to what we will do with it in the future...
A private and undocumented API doesn't do much for the people who develop or rely on one or more of the several hundred (thousand?) iOS apps that already integrate Dropbox.
To clarify, there are definite plans to document and release the Copy API. The only thing we can't make promises about is when that will happen (soon?).