It seems a lot of people are really in the dark about /i/ and 4chan's love/hate relationship. This won't have all the details, but should serve as a good enough summary.
After moot created the "new rules" for /b/, cracking down on jailbait and "call-to-invasion" threads (commonly referred to as /b/day), 7chan opened an "/i/ - Invasion" board to hold the refugees. Here, those banned or alienated from 4chan were able to do their raid organizing.
After a while, 7chan's admin was given an ultimatum by his host, who had received many complaints from other websites that /i/ had targeted. They were violating the TOS, and decided to remove the /i/ board instead of finding a new host.
Afterwards, 420chan hosted /i/ firstly on its own servers and later only linked to the board, having moved to a separate host: not420chan. Due to the nature of /i/nsurgent activity, these boards have a limited lifespan, so they moved their main operations to IRC so they could better communicate and plan in a less public way. After this they weren't "affiliated" with any particular chan, though they certainly lurk them all; most have a hatred for 4chan and love for 420.. 7chan is somewhere in the middle.
The #insurgency IRC channel was on Rizon for a time before moving to their own network, "lulznet" - not to be confused with lulz.net. 7chan at one point linked their IRC network with /i/'s. The /i/nsurgents also asked moot to join, and when he ignored them, they launched a distributed denial of service attack against 4chan. 7chan de-linked from their network.
During and after the downtime from the DDoS, as many Anonymous were trying to understand what happened, /i/ was spreading misinformation on the various imageboards and Encyclopedia Dramatica about who was responsible. This ranged between the lulz.net furries, some (not SA-related) "g00n" hacker group, another named "teamloosh", the GNAA, and so on.
Thus, it is not surprising to again find these same traditional scapegoats being blamed for the DNS hijack. The /i/nsurgents will probably continue to harass 4chan until either moot gives up on it or their group is dealt with by law enforcement - the latter being more likely even if still a low chance. An alternative would be for /i/ to find something more productive to do with their time, but if the Internet has taught us anything, we shouldn't hold our breaths on it.