Well, being the DNA curmudgeon that I am, I'll state first that I've never seen any valid autosomal DNA evidence via triangulation to a birth occurring in the 1600s. So being curious, I ran the cited kits at GEDmatch.
I believe it to be a simple misunderstanding as to what autosomal DNA triangulation is (and of course we still don't know to what level, meaning how many generations, or birth events, the methodology might even be valid). The three individuals do not triangulate; in fact, they share no meaningful segments even on the same chromosomes.
The very small segments, one of which is accounted for by only 188 matching SNPs and is very likely false, are on chromosomes 6, 10, and 13; the single Chromosome 6 segment includes a known high-pile-up region. Without using the kit numbers, the matrix looks like this:
||Chr 13, 7.6cM 188 SNPs
||Chr 10, 10.4cM 291 SNPs|
||Chr 6, 8.1cM 457 SNPs|
Two of the individuals show as being 7th cousins 1x removed. The probability of any two people related at that level sharing any meaningful autosomal DNA is 0.575%. Which puts the odds at 173:1 that any two test-takers who do actually descend from the shared 8g-grandparents would show a real match. If any valid IBD segment has hung around that long, it won't be traceable to a specific MRCA; it will be common to a very large number of individuals who share a broad haplotypic ancestry going back many generations, likely before the genealogical timeframe.