Good poast. The only things I would mention is the following:
1. As you point out, your experience isn't the only type of experience. But your experience does mirror the feelings of, say, undergrad students not from NC, who come from the North. Duke is going to obviously feel like the biggest rival. This is exacerbated by the fact that Northeasterners don't care for college football (the sport in which the rivalry with Moo is the most heated), and the fact that the UNC campus vibe is all about basketball, which is where we have the strongest rivalry with Duke.
2. You bring up a good point about Duke/UNC collaboration. They work together on a lot of stuff, which certainly links the schools closer together, than UNC/Moo are linked, as universities.
3. You mention your views are different than those of "someone born in the Triangle." Remember, there's much more to the state of North Carolina than the Triangle. In fact, the Triangle is a MUCH different feel than the rest of the state. The Triangle is much more progressive, much more transient, and much more liberal than the rest of the state (Asheville excluded). That, IMO, helps the Duke - Carolina rivalry as well. Socioeconomically/politically, Duke and Carolina are more similar than Carolina and Moo.
4. But, like
@tarheel0910 and I have pointed out, a big aspect of a rivalry is the 'house divided' aspect. And that simply doesn't exist with Duke-Carolina. A family from Long Island is much more likely to have a Carolina/Duke house divided than a family from Charlotte or Greensboro or Shelby or Wilkesboro or Laurinburg, or Roxboro. Instead, families from all those towns and all over NC are much more likely to have a Moo/Carolina house divided. That's why I state that the UNC - Duke rivalry is centered around competition and winning championships. The UNC - Moo rivalry is centered around hate/local fandom. Duke is closer to UNC, geographically. But Duke might as well be 8 states away from UNC in terms of local ties.