...except that both Ubuntu 13.04 and Ubuntu 13.10 uses python-gpgme 0.3-0ubuntu1 0
Instead I took at look at libgpgme11.
Downgrading libgpgme11 from the current Ubuntu 13.10 version 1.4.2-0.1ubuntu2 to the Ubuntu 13.04 verison 1.2.0-1.4ubuntu4 did the trick, and allowed Dropbox to verify its downloaded binary without complaining.
...except that both Ubuntu 13.04 and Ubuntu 13.10 uses python-gpgme 0.3-0ubuntu1 0
Instead I took at look at libgpgme11.
Downgrading libgpgme11 from the current Ubuntu 13.10 version 1.4.2-0.1ubuntu2 to the Ubuntu 13.04 verison 1.2.0-1.4ubuntu4 did the trick, and allowed Dropbox to verify its downloaded binary without complaining.