I have lots of friends at Duke, and I've had a bit of exposure to their Greek system through them. The impression that I get is that, in recent years, Theta Chi has really been struggling with numbers (they lost their section on campus a couple years ago because they repeatedly failed to fill it) and that, no matter which way the chapter is trying to paint their motivation, it's probably more of a "you can't fire me, I quit!" kind of move in regards to their national.
As far as Eta Prime and what used to be Delta Phi Alpha, they were chapters of Kappa Sigma and SAE that disaffiliated with their national after being threatened with sanctions - Kappa Sigma had a pledge hospitalized with alcohol poisoning and then an intoxicated brother fall from a window when they were supposed to be dry (
link), and SAE, among other serious issues, had a 16 year old girl allege that she was raped while attending a party there (
link). However, this does not seem to have remotely stunted their recruitment and socialization efforts, especially the latter. As you can see in the Chronicle article, every time either is mentioned, it is always "Eta Prime - formerly Kappa Sigma", etc. so they retain the informal recognition that way. The school has also made a practice of sending letters to the parents of freshmen warning them about these unaffiliated fraternities, which of course heightens the "forbidden fruit" factor. Yet, they never seem to have any problems recruiting or mixing with the well-regarded sororities on campus, however against the rules that might be, and Eta Prime even enjoyed some notoriety last year after several women were found baby oil wrestling in the basement of their off-campus house when police came to investigate a noise complaint. However, I do find it interesting that Delta Phi Alpha has decided to pursue affiliation with a national fraternity in spite of their insisting for years that they were getting along fine without one.
Anyway, sorry for the long post, just wanted to shed some light on the "off-campus fraternity" situation at Duke since I know a little bit about it. It just seems to me that this is less of a rebellion but rather more of a desperation move on the part of this chapter, but that's just me speculating.