One issue with the experiment is it has such a narrow use case. Disappearing after one download / 24hrs makes sending a file to multiple people--or just one person who drags their feet on the DL-- makes it really inconvenient to use. Even offering "1 download -OR- 24hrs" would make it far more useful.
There are other existing solutions like https://share.riseup.net which do not do things like this too and which do allow multiple downloads.
Do they communicate that sending any known file is non-private?
If I email myself a pop-song, does the client automatically start the extradition proceedings for the RIAA; or does that come later? /s
Also, you wouldn't need add a file. Zipping it alone would be enough to change the hash.
I don't think you can expect the file mod time to be identical, as it isn't preserved through many forms of file distribution.
[1]https://en.wikipedia.org/wiki/Zip_(file_format)#File_headers
Why would they do that? It's not like anyone can send them DMCA notices: the act of verifying that the upload violates your copyright already removes the file from the service. And I don't see anything in the DMCA that requires them to search for offenders, they just have to act once they become aware?
The Megaupload case sadly is a good example of what no one wants to repeat, as there this was exactly argued - that, once notified, the hoster has to ensure this file won't ever be uploaded again, and all other copies are removed, too.