Shared access is never a feature of SAN, but a feature of file system. This is exactly the reason why shared storage in Hyper-V is built on CSV (Cluster Shared Volumes), and not just regular NTFS volumes. CSV provides reservations required for shared access to the same iSCSI target by multiple hosts.
I am a bit confused by the discussion because first you are asking about connecting a host and a backup proxy to the same target (this is fine, as backup proxy does read-only access), but then the discussion switches to connecting multiple hosts to the same target (this requires CSV to manage write access from multiple hosts correctly).
In short, answering your original question, your SAN is very "real" and you can implement anything you want with it.