Negative Feedback Factor
I just don't seem to comprehend how this negative attenuation is
  accomplished just using resistive networks


There are some reasons why this can happen, and in fact happen all the time:


The output signal polarity may be reversed (or have enough phase shift) due to the plant transfer function. When you take a sample of this signal you can feed it back to the input directly because it already is negative feedback.
If the plant transfer function doesn't reverse polarity, then the injection point of the feedback at the input may reverse it instead, thus having the same effect. That's the reason why we use the negative input of opamps for feeding back the output, for example.


These situations are effectively equivalent to what you call "negative attenuation" and are used extensively in amplifier design, etc.