How exactly do you get that multi-TB backup onto the database server's disk so quickly? Even with a gigabit network interface, that's only 125MB/s, which is over two hours[0] to transfer 1TB. Even if you have a 10 gigabit network, that's ~13 minutes[0].

Also consider if the backups are compressed -- a 1TB compressed file also takes time to uncompress. If the data compresses well, you could even run into the disk being the bottleneck, not the network.

[0] Well, more than that; those numbers assume you're actually getting the link rate with no overhead, which of course isn't reality.