Our only alternative appears to be providing TextExpander data via x-callback-url. User action will be required to acquire and update snippet data. Each app will have its own copy of the TextExpander data, which will not sync automatically with user updates made in the TextExpander touch app. It's not ideal, but it is within the App Store Review Guidelines. It also means users won't lose TextExpander touch support in your app.
It's sad, but I think it was inevitable. Syncing data through corners of the OS like Contacts or Reminders always felt a bit at odds with Sandboxing. Knowing nothing about the TE or Dropbox SDK, I am curious why they just don't sync snippets that way. I sync over 2000 text note files with 3 different iOS apps on 2 different devices without a single problem.
I know people will be angry at this enforcement by Apple, but I'd suggest looking at it differently. This is a time for Smile to improve the way TextExpander works and perhaps improve their business model. I use TextExpander like crazy but it's boxed in by the current design. This is made painfully obvious by the Editorial snippet and workflow system. Today, I rarely open the TextExpander app, so it primarily exists for the SDK. Just like Dropbox on iOS.