Well, you're setting a low bar. DropBox is not secure from the government in any way. BTSync is better.

If I understood the article correctly, an MITM attacker (or federal agency) could in theory know that you have a copy of a file only after they have a copy of the same file themselves, by comparing hashes.

Well with Dropbox you know that the government can request any data presently or previously in your folders. With btsync it doesn't seem to be so easy because data isn't stored centralized, but there are some potential leaks. Still better than Dropbox.