What is the purpose of an app disallowing backups (android:allowBackup="false")? 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.
You don't need root to backup data from an android device to a PC, you only need physical access and to enable debugging in the developer menu. This lets you copy data from the app's internal storage, which may contain sensitive information that you don't want to let somebody steal, like your facebook access token.

I agree that it is pretty trivial in most cases, but there are some cases which require this extra layer of protection against attacks where physical access is involved.

Note that in order to get around this you would need to root the phone, in which case the sensitive data in the internal storage would be wiped when the factory reset occurs.