According to this answer : https://stats.stackexchange.com/a/37710/138097
I understand the logic, except following sentense: [ note: because of sufficiency, we have reduced the problem of showing uncorrelatedness with every estimator of 0 to only have to show it for estimators that depend only on T ]
What about the other statistics that is unbiased estimator of zero but not depend on T?
Is there something that i missed about "because of sufficiency" ?
