Sherry, for many biological and mathematical reasons, with autosomal DNA you are quite unlikely to find verifiable matches beyond the level of 5th cousins. Here's another chart to glance at. And the work by Dr. Tim Janzen in looking at trio-phased individuals found that a 7cM segment was false-positive 58% of the time, not 53%. If almost 6 in 10 reported matches are false, is it throwing out the baby with the bathwater, or simply taking reasonable steps to make certain that the baby in the bathwater is our own? Down at 5cM, almost 9 out 10 of the babies will be someone else's. I know; world's absolute worst counter-analogy. 
In my comparisons using a 2.08-million SNP superkit at GEDmatch along with 11 of our common microarray test results of the same DNA, the worst performing common test--one of the current ones--showed, with default settings and a threshold of greater than or equal to 10cM, 2.1 matches for every one displayed as matching the far more extensive superkit. This is by no means conclusive, but it implies that, with more unique SNPs tested for comparison, even at 10cM more results at GEDmatch could be false-positive than not, that small segments have been conflated as being one continuous range of half-identical nucleotides when, in fact, the reported segment is broken somewhere by a mismatch because our typical autosomal DNA tests look only at about 0.02% of our DNA...and any two tests might be examining as few as 17% of the same SNPs.
The SNP count does definitely matter...but it's the SNP density, not the total number, as well as which SNPs and where they're located. Too, GEDmatch recently lowered their default "SNP window size threshold" yet again. Prior to GEDmatch Genesis the minimum was 700 SNPs; with Genesis going into production, that became a dynamic range between 200 and 400; now it's "about 2/3 of segments will have between 185 and 214 SNPs." I consider the original 700 reasonable, but the modifications were made because, with the introduction of the Illumina GSA chipset, we began having a range of different microarray tests that overlap on only a minority of the same SNPs. In order to keep reported match numbers up, GEDmatch decreased the SNP density requirements.
With a very broad brush, 1cM will be approximate, with a lot of flexibility based upon chromosomal location, to about 1 million base pairs. At that relative density, there should be just over 200 SNPs per centiMorgan. Anything much lower than that means fewer SNPs have been examined in a comparison between two tests than the approximate physical average tested across the genome. Caution should be applied. If you see, for example, a 7cM segment reporting 300 matching SNPs when the genomic average should be closer to 1,400, there may be a problem.
Our microarray tests look only at about one marker in every 4,800 base pairs of nucleotides, on average. That relative SNP density is an element that can provide us a bit of confidence that we're doing enough apples-to-apples matching for the outcome to be meaningful. If there's a relatively long stretch in the raw data where SNPs are simply assumed to match but were not tested, that can lead to mistakes. At the bottom of the GEDmatch free one-to-one autosomal comparison tool is a little checkbox to "prevent hard breaks." I recommend that be kept unchecked. The distance allowed between matching SNPs of up a half million base pairs is excessive.
Jennifer, DNA is absolutely just another piece in the puzzle. That's something a lot of people forget because it looks all "sciencey." But it's a form of evidence to be evaluated and weighted just like any other. It seldom gives us a binary yes-or-no result. Other than for twins, parents, and full siblings, the data has to be rigorously analyzed. But--and there's a catch--it's unlike any traditional form of genealogical evidence we have ever used and it requires a different skillset to analyze. I've written over 1.4 million words (literally) of stuff here on G2G over the past six years, 95% of it about DNA. You can browse some of that and decide if I have any idea whereof I speak.
As a mini-experiment, if I use the GEDmatch free one-to-one tool at the default settings and compare your kit against my WGS superkit, predictably I get, "No shared DNA segments found." If I leave it at 7cM but drop the SNP window down to 100, I still get no shared DNA. At 5cM, no shared DNA.
But if I use my 23andMe v5 test kit, which has few in-common tested SNPs with your AncestryDNA results, and leave the centiMorgan threshold at 7cM but move the SNP window to 100, we end up showing 15.2cM shared over two segments. If I then move it to 5cM and leave the 100 SNP window, we show 36.7cM total across six segments. Dropping it all the way down to 3cM and we come in with a whopping 106.5cM across 25 segments. Every one of those comparisons is a false-positive.
GEDmatch gives us a granular level of control over most of their tools, but that doesn't mean it isn't simple for us to make the results into a fabrication. Our goal should be to employ the most objective and realistic data we can find, and then to analyze it closely. Trying to make the data fit a desired outcome is the very opposite of the scientific method. Or of the Genealogical Proof Standard, for that matter.
I didn't mention it in my first post, but extending the examples, there is an issue with the kind of test Susannah took that makes her matching results at GEDmatch more difficult to interpret. Genes for Good use a microarray unlike any of the companies doing genealogy testing. Their principal interest is medicine and pharmacology, so while they test more SNPs than any other of our standard companies (almost 744,000), only about 250,000 of them are not exonic markers...meaning that all but those 250K are related to protein coding genes or their flanking or control regions. Other than genes that involve phenotype, like hair and eye color, the rest of those are going to be 99.9%+ identical among all humans. We all have the same neural, cardiovascular, and musculoskeletal systems, for example.
By contrast, even though from around 10% to 18% of the SNPs our genealogy tests look at are exonic markers, that still leaves us on average with about 500,000 SNPs to compare that have more relevance to population genetics. Having half as many meaningful markers in the Genes for Good data definitely, at least at GEDmatch, leads to an increased possibility of false-positives. If I run my 23andMe v5 kit against Susannah's kit at the 3cM, 100 SNP window, prevent hard breaks settings, the result is a humorous 238.8cM over 56 shared segments. If that total amount were over a dozen or fewer segments, that would make us 2nd cousins.
About 10 days ago here on G2G I provided a summary of some the steps I go through to evaluate the validity of small segments. It isn't that they're de facto always false. But they're sorta like the FTX crypto-currency guy trying to sell you an expensive investment that he guarantees will increase over 10-fold by next Monday: approach with skepticism. Again, just like in lab research, the primary objective is to attempt to disprove the hypothesis, not prove it. The real battle is to always avoid confirmation bias.
