By itself, a network cannot act as backup media. But combined with mass storage technologies, it can serve quite well. For instance, by combining a high-speed network link to a remote data center containing large amounts of disk storage, suddenly the disadvantages about backing up to disks mentioned earlier are no longer disadvantages.
By backing up over the network, the disk drives are already off-site, so there is no need for transporting fragile disk drives anywhere. With sufficient network bandwidth, the speed advantage you can get from backing up to disk drives is maintained.
However, this approach still does nothing to address the matter of archival storage (though the same "spin off to tape after the backup" approach mentioned earlier can be used). In addition, the costs of a remote data center with a high-speed link to the main data center make this solution extremely expensive. But for the types of organizations that need the kind of features this solution can provide, it is a cost they gladly pay.