Very important points.
I would say that the concept of a "pedigreed negative" is a farce to begin with. Conceptually and practically, it is almost impossible to conclusively show that something is truly negative. There are countless ways -- some known, some not -- in which you can fail to find something that is actually present (wrong assays, assay failure, wrong conditions, sample preparation, etc, etc). Labeling something as "pedigreed negative" after looking at it using one method (shown repeatedly to be inadequate) is nothing short of fraud.
At most, these samples can be said to be "pedigreed negative" for only the exact methodology used to pedigree them. Even saying that assumes many things (that the assays worked when the samples were pedigreed; that there is no transience of positivity across samples from the same source).
The concept of a "pedigreed positive" is tricky too, but for different reasons. The issue here -- especially with new discoveries -- is showing conclusively that you are finding what you think you are finding. However, conceptually, this is much different than "pedigreed negatives" because you only need to conclusively demonstrate one positive thing as opposed to ruling out countless negative variables. Demonstrating consistent positivity of a sample using multiple methods is usually sufficient to ensure that something is indeed positive. Even then, issues of transience and detecting near the limits could mean that a "pedigreed positive" isn't always positive.
So while both types of pedigree have conceptual hurdles, "pedigreed negatives" are significantly more difficult -- if even possible -- to ensure.
Of course the denialobots have been all over the place harping about how "there is no such thing as a known clinical positive" (i.e. "pedigreed positive"), yet they are palpably absent in the face of the far more egregious conceptual flaw of the "pedigreed negative."