A filesystem snapshot is only reliable if you stop the database to do it, or if there is some sort of cooperation between the database and the tool that triggers the FS snapshot creation.
File system and LVM snapshots are atomic, so if you cannot get a working database from that your database won't survive a power failure either. You can also do a file system backup of PostgreSQL without atomic snapshots but then you will need to inform PostgreSQL of the backup and then copy files in the right order. The pg_basebackup tool and various third party tools handle this for you.