Go get a 1Gbps link and try to download 24/7 for a month. See what you get. Averaged, it'll probably be around 800Mbps, or 260TB. Latency exists.
(If you're really lucky, you might be able to get 900Mbps or so, but that's not likely: the max throughput on 1Gb Ethernet is below 950Mbps, even if you had packets flowing continuously!)
The supposed quote says "We’re writing to you today because of your traffic use, which currently averages above 250 TB/month on some of your servers."
It averages on multiple of their servers, which indicates to me that the average was taken over the course of some months (?). They may well have reached 320TB in some months on some servers.
I'm not surprised by this. For me, unlimited traffic (with 1 gbps) means i can spike in some months without having to worry about costs exploding, but if I'm maxing it out consistently, then I might be asked to move to a different service or upgrade.
