I'm asking specifically because Helium (the application formerly known as Carbon) uses root permissions to do data backups and with root I can manually (through the shell or Root Explorer) back up data for apps that disallow it. So why would some app data not backup with Helium (which has root privileges granted)?
I read the information about the permission elsewhere on SE as well as at developer.android.com that says user couldn't copy off data to dig through on their PC, but it's actually trivial if you have root access in the first place. If you're really into digging through data then bypassing the permission is trivial. If the permission would stop you, you probably wouldn't be the type to be digging through app data.