You are right that a full virtualization technique like KVM makes it possible to run a customized networking stack, file system, etc. without being root.
Virtualization is the key, but the main difference is granularity.
Each Hurd subsystem is virtualized, meaning that as long as you implement the subsystem's interface, you can replace the default subsystem instance. Compare this with running a complete GNU/Linux system in QEMU/KVM with its own file system image, etc.
The Hurd's approach allows for selected sharing. Just because process A uses a different networking stack than process B doesn't prevent it from accessing the very same files, communicating with B over a pipe, mapping pages from B's address space into its own, etc. Conversely, sharing among full-blown GNU/Linux VMs is much harder.