How does Dropbox actually protect against sharing copyrighted content?

This TechCrunch article discusses how Dropbox uses hashing to check whether you're sharing copyrighted material "without actually looking at your stuff." Specifically, they offer the following (unsourced) "official comment" from Dropbox:

There have been some questions around how we handle copyright notices. We sometimes receive DMCA notices to remove links on copyright grounds. When we receive these, we process them according to the law and disable the identified link. We have an automated system that then prevents other users from sharing the identical material using another Dropbox link. This is done by comparing file hashes. We don’t look at the files in your private folders and are committed to keeping your stuff safe.

The hash-and-compare strategy sounds like a reasonable idea, but easily thwartable. What's to stop me from creating seed.txt, a text file with some random contents, and zipping that together with copyrightedContent.mp4 to create innocuousArchive.zip? Or, if they expand archives, adding a bunch of random (or zero) bytes to the top of the file itself?

(The purpose of this question is not necessarily to determine how Dropbox itself actually does this, but rather to explore different ways to do this in general—or whether it is feasible at all.)