At least for the time being, iOS apps that use the Dropbox SDK submitted to the iTunes App Store are being rejected. This was first pointed out by The Next Web.
This allegedly has to do with Apple’s policy of disallowing apps that enable users to purchase things outside of the application, not the fact that Apple could consider Dropbox a long-term competitor.
Here is Apple’s official statement on the matter:
We found that your app provides access to external mechanisms for purchases or subscriptions to be used in the app, which is not in compliance with the App Store Review Guidelines.
Specifically, your app enables a user to create accounts with Dropbox and Google.
Apparently, Apple is working with Dropbox on a workaround to this issue. Last month, Dropbox also got a fiercely competitive entry to its space in the form of Google Drive.