what pstring said.. it may be your truss rod. Ok,it is V.unusual to get truss rod inflicted buzzes this "high" up the neck, but it's not unknown. Personally I would check to see if the string is hitting or rubbing on the 4th or possibly 5th fret. if that's not the case try slackening the truss rod- say 1/8th of a turn and see how you go.
:)
Accuracy,you say? hmm interesting concept..