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I've always thought that a CFI could do the Private instrument flight requirement.
[/ QUOTE ]You always thought correctly. The difference with the private and the others is that the FAA doesn't call it "instrument training".
For example, compare the instrument requirements for the private with the ones for the commercial and you will see the difference. The private one says, "flight training ... on the control and maneuvering of an airplane solely by reference to instruments" which can be done by a CFI. The commercial one uses the magic words "instrument training" or "instrument instruction", which requires a CFII.
And it's not "muddy" at all. The FAA has been making the distinction between the two for a long time. Here's a blurb from a 25 year old FAA Legal opinion
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Since Section 61.65(e)(2) refers to "instrument instruction" by an authorized instructor, the instructor must have an instrument instruction rating. Section 61.107 refers to "instruction from an authorized instructor" and to "control and maneuvering an airplane solely by reference to instruments," rather than to "instrument instruction;" therefore, any certificated flight instructor (CFI) may give the type of instruction described in FAR 61.107.
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