3TB/day is about a third of what you can serve out of any run of the mill PC with a gigabit ethernet connection. There are 22TB drives and individual servers with 24 drive bays, which exceeds 500TB. So you could do this with one machine connected to a gigabit fiber connection, and the machine would cost approximately what they're paying monthly (almost all of that for the drives).
In practice a 24-bay chassis is silly and you might use a separate storage array etc., but that's just details.
> Plus, even if you deal with the storage itself, how do you deal with serving the traffic globally?
At 3TB/day you're not Netflix. Just serve it directly from your own server.