On second thought, block devices are sort of sketchy for this use case - but FUSE still seems like a perfectly natural way to export networked storage.
I'd expect a backup hierarchy to just be a directory of read-only snapshots of my files - I mean, this is how I organize backups locally either way (e.g. /snapshot/YYYY-MM-DD/etc/whatever.conf).
The advantage of using a standard API like filesystems and FUSE is that you can use it easily and from the terminal without needing to deal with bloated GUIs and JVMs that are no doubt hard to install, hard to use and hard to rely on.
A JVM is also a pretty hefty requirement to have on a machine. (I personally avoid installing it all costs, mostly because everything that targets JVM seems to be crud to begin with)
I'm pretty sure the CrashPlan client a .jar, so you just need a jvm, thus broad OS compatibility.