Good word, miscommunication. And miscommunication is usually diminished to insignificant levels with dialectic conversations between knowledgeable people.
Thank you for your cogent presentation on the subject of triangulation. It is too bad this is not the forum for an extensive conversational dialectic on the matter. But I would enjoy it.
Sometimes I think we forget the forest focusing on the trees, or even worse, the root system of an individual tree.
That said, I offer a simple outline of points regarding genealogy and DNA below.
1. First, there is a family tree. Otherwise, the subject is beyond the scope of genealogy.
2. The most important thing is having an accurate (hence the need for WikiTree) and, if possible, comprehensive family tree. Otherwise, what is the point?
3. In the absence of accurately developed family trees, the viability of DNA Genealogy is diminished.
4. Y-DNA, mtDNA and auDNA are all important and useful tools in genealogy, for different reasons, but only if one establishes an accurate family tree.
From a genealogy perspective, Y-DNA & mtDNA have limited, but useful, value.
The value of Y-DNA is limited to the unbroken length of the paternal male line-short or long. And, it is limited to one paternal male line.
The value of mtDNA in the maternal female line is that unbroken lines are not an issue from a DNA perspective. However, in patriarchal societies, finding mothers may be more difficult as there is no singular surname to focus on.
For the remaining 14 lines within a family tree at the 2nd ggp level, auDNA is the only means of validating DNA relationships within those lines. The question becomes how to identify auDNA matches within that group, and the other two lines as well.
Ignoring multi-generation tests within the family tree, the limit is generally to the 5th great-grandparent level. That may be achieved by capturing as many descendants of those 5th ggp's within the family tree as possible.
At that point the law of large numbers comes into place. However, it certainly makes it easier if DNA matches have accurate family trees as well. At a minimum, most people can identify their siblings, parents, grandparents, etc. as applicable.
While auDNA accuracy may be in question at the higher ggp levels, if one has an accurate and exhaustive tree - then identifying common ancestors is much easier. Then the accuracy of auDNA testing at that level is not necessary. (the caveat is that one cannot ensure a DNA relationship exists at that level. However, a genealogical and familial relationship did exist. Again, the law of large numbers and parentage probabilities would suggest a fairly high confidence level of biological relationships in the overall tree.)
While auDNA is not necessarily accurate at the 100% level, what are the odds that a common ancestor is not the common ancestor from a biological perspective?
Take those odds against 20-110+ collective DNA matches for a 5th ggp common ancestor and one has a pretty good case for saying they have validated that line in their family tree.
Besides, with current DNA technology, who is to say differently?