This was much more than garden variety " Dutch Roll". The yaw damper had a broken part that made it out of sync with its inputs, making the rudder actually accentuate the yaw instead of combatting it. At the end they say the rudder was basically moving rapidly back and forth, uncommanded, and broke the tail off the aircraft. The top of the vert stab was moving something like +/- 8 feet from aircraft centerline when it finally broke.
You can turn off the powered rudder in the Tanker, which would have instantly fixed the problem. But this scenario has never been trained in the sim, and the scenario used in the sim to trigger the Rudder Power Off scenario is a rudder Hardover, not occilating back and forth. The sim didn't even have this type of scenario as a selectable malfunction.
They also found something like 15 checklists that referred to unwanted rudder inputs. Some of the names of these checklist are very similar, such as Rudder Hunting, Rudder Snaking, uncommanded Rudder ( this one contains the boldface Rudder Power Off), yaw damper failure, as well as procedures for combatting Dutch roll, which they were actually doing when the aircraft became divergent.
Personally, in addition to the crew's lack of exposure to the scenario, I think the way the Tankers manuals are written played a part. Every "checklist" and I put that in air quotes, is paragraphs of text, first describing what you have, then it talks about consequences, then maybe it gives you a remedy. They are by far the worst manuals I've seen in my 4 military planes and 3 civilian ones. I've heard that there has been multiple offers to come up with a civilian style QRH, but big blue says it cost too much.