Weirdly it does have dedicated servers, they handle things like events, scheduling, fireteam handling. It also uses p2p for your interaction with other players. Theres also a p2p host that helps coordinate.
Pretty complex, I'll need time.
An example of this is Crota. His events were handled by the host. If the host disconnected when Crota was kneeling, he would stay kneeling. This was then exploited pathetically for l00t. Crotas timer was moved to the servers, but the damage was done.
Ammo crates and doors are not events, they are handed by the host, so in extreme cases of lag doors won't even open or ammo crates can't be picked up in PvP.
To make it more fun, the host changes every 3 mins. So lag can come and go in a match.
You might be able communicate with me faster than we can both communicate with a server in Seattle. I can understand the approach, however it didn't stop me swearing when coming up against a Iraqi clan with an internet speed as fast a telegram.
BTW, when IB is on, go play normal control or clash... All the high ranking players are in IB, so crucible is easier.