Server: Okay, tell me what byte 1257 (randomly chosen) of that file is and I'll mark you as having the file.
Client: Ummm ...
For a <4mb file, if you just guessed a random byte and try 256 times, wouldn't you probably get it right at least once?
Still, they could easily change the scheme to ask for more bytes to reduce the chance of a correct guess, plus it would be hopeless for large files.
That doesn't really scale, no, but sharing hashes doesn't really either, unless you want to spend a significant amount of time building infrastructure to keep track of who has what files and automate the management of sharing hashes.
That post made it sound like there was a purpose to having the file in dropbox other than getting it.