You are quite correct. Bungie made a presentation at GDC 2015 in which they explained the network architecture of Destiny. Here's the link:
[url=http://www.gdcvault.com/play/1022247/Shared-World-Shooter-Destiny-s]Shared World Shooter - Destiny[/url]
This server you have observed is an "activity host". It does not run any simulation (that's one of the consoles in your P2P network, designated the "physics host"), it just runs scripts and maintains the consistency of shared information.
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Just read the mission statement. It matches up with what I was thinking pretty well. I only wish they accomplished the "low latency", and "seamless" goals in the mission statement.