Personally, I think someone's getting mixed up, here (could be me, though!).
AFAIK, inverting the signal is actually what allows negative feedback. If the signal was not inverted, a feedback connection back to the input would blow up, become unstable, runaway, etc. It is the inversion of the signal that allows the feedback loop to close, and thereby work. In other words, the music signal is inverted by the OPA551 opamp in the NuTube Millett Hybrid circuit. That signal becomes negative. It's then fed back into the input side of the opamp as a negative music signal. Now the opamp has two signals that are input, one positive and one negative. The opamp is then able to compare/correct to minimize the voltage offset between the two. That minimizes distortion and noise. As I understand it, that's how negative feedback works.
I am not familiar with Nelson Pass's Korg preamp, but if it is simply an amplifier circuit without feedback, I'm guessing that trying to eliminate the signal inversion at the input to the NuTube hybrid is not the way to go about creating a zero-feedback circuit.