I guess these are different problems: of course if I launch a snapshot without freezing the filesystem (via fsfreeze or xfs_freeze or so) the snapshot may be unconsistent and require a fsck (and it may loss data). So, this is the cause for shutdown recommendation. But, snapshot process should be, in any case, “asynchronous”, that is, you launch it and in less than a second instance should be available again and snapshot should be available later, when possible (may be queued state).
This is the behaviour, for example in AWS. I understand the problem may be related with underlying virtualization used and/or disk management software.
According this, “live snapshots allows you to create new images from running instances […] These snapshots are simply disk-only snapshots. Snapshotting an instance can now be performed with no downtime (assuming QEMU 1.3+ and libvirt 1.0+ are used).”