First, I don't think that the Hakuho/Chiyotaikai should just be ignored. It feels like ignoring a sample that doesn't agree with the theory. That means that it's either 7 wins in a row for the needy Ozeki or 9 of 10.
One thing I noticed when looking at the database query was that 3 of those 7 matches were Kotooshu beating Chiyotaikai. It occurs to me that Kotooshu has dominated Chiyotaikai head-to-head, so maybe seven in a row isn't really a big deal.
What I came up with was a terribly rough and quick way of putting a percentage of winning for the needy Ozeki, by taking their head-to-head record at that time. Obviously, there is a big problem with taking lifetime stats which could be accumulated over years and applying them to the present(Kotomitsuki should be considered a bigger favorite against both Kaio and Chiyotaikai than the head-to-head data would suggest, for instance), but it gave me some idea.
Taking the chance for all seven and multiplying them together, you get a 1.9% chance of everything happening as it did.
Obviously, there is a selection bias here, counting from the beginning of a streak, and seven is still a rather small sample size. Something of this probability could happen innocently, or there could be another reason for why there seems to be a greater chance of victory(a greater desire to win, obviously).
If this is true, why is it a recent development? I'm sure people can come up with a number of explanations, so I'll throw in one. Kosho. Maybe when the Ozeki couldn't safely withdraw due to injury, they decided they needed something else to maintain their rank.
I think that cooperation between Ozeki does happen, but I also don't worry about it too much. What I know, though, is that the information Kozaru brought is at least worth more discussion than being lumped into the same category as saying that Asashoryu needed to buy 11 of his victories in one basho.