I would lean toward the latter more so than the former...
Apple is all about simplicity. Can you imagine the soccer moms when a finder window popped up asking them what app they wanted to import the file into?
Thats the thing though..they can simplify finder as a concept.
Imagine a simple app that has a flat filesystem structure (no folders). You can open the app itself and see your grid of files, and just tap to open it. If you have multiple apps that can open a file it lets you choose, and set as default for next time. A search bar up top and the ability to sort in different ways (By date, type, name.) And the final thing is simple tagging (So I can tag something as "business" or "school", but you can have multiple tags on a document.) Tagging would be completely optional though and only necessary for users with a lot of documents on their device.
Apps get an api to access these files (With the same looking interface that pops up), and when they show the list it will only show the filetypes they support (So Pages only shows doc/pages, numbers XLS/CSV/numbers, etc.)
And finally the huge advantage that this brings - You can finally attach files to emails that aren't pictures.
That is what I want. Get rid of file duplication. And of course the old "Open In.." menu would still work as it does now, but apps would have a path to go on for the future.