I'm with ya, Shirlea. Ancestry could have vastly improved that wording; I have no doubt that everyone who's looking at the new display of "Longest Segment" for the first time is thoroughly baffled. Seems to me like the simple addition of a couple of words would help. Maybe like:
- Genealogically Significant Shared DNA: 6.7 cM across 1 segments
- Longest Overall Segment: 17 cM
May still not be clear enough, but you're absolutely correct: when you see that odd disparity between "Shared DNA" and "Longest Segment," it's the result of Ancestry's application of its proprietary Timber algorithm to "assess informativeness of matches for relationship estimation." Their new July 2020 "AncestryDNA Matching White Paper" is here if you want to browse through it (see section 4 for their description of Timber; and BTW, this is the most forthcoming they've ever been about the calculation method itself): https://www.ancestrycdn.com/support/us/2020/07/2020whitepaper.pdf.
So, yeah: in essence what the numbers you noted mean are, "Hey! Good news! We found a single 17cM IBD segment in common between the two of you, but we've decided that only 6.7cM of it are valid when we're talking about genealogy. The rest of the 17cM segment occurs too frequently among our other samples of a similar haplotype (which means a global-population or haplotypic pile-up region), or that may include areas of protein coding genes that don't change much from one generation to another, or where we see way more DNA sharing than we would otherwise expect and it's showing up in areas where there isn't a lot of usable SNP density, like some areas at the chromosomal ends, the telomeres, or close to where the pair of chromosomes join together, the centromere. So your important, genealogically meaningful match is only 6.7cM of what, in the results, otherwise looks like a 17cM segment."
Which is just a tad too long to show on your matching page. 
But there really is a method to the head-tilting confusion. And one, from the standpoint of genealogical accuracy, I can't really quibble with. I do, though, still sorely wish that Ancestry would display all that detail to us: actual segment start/stop loci; which portions of a segment determined to be IBD was excluded from matching and why (at least a few general "why" categories; and the ability to compare, with that detail, more than two individuals at a time. A chromosome browser would be nice, but I personally never bother much with the graphics anyway.
Ancestry does genotyped, computational phasing, and they attempt to eliminate blocks of DNA that would be useful for anthropology and population genetics but that aren't meaningful for the reach of autosomal DNA for genealogical matching. They're the only company that does that, and as a result I tend to trust their final matching more than elsewhere.
That's one failing we as a community currently have: GEDmatch does no culling of SNPs (other than, I believe, avoiding a very few SNP-poor areas on certain chromosomes) and they do no imputation as a method to improve validation of IBD segments. Which is fine, except...that leaves everyone to their own devices to collate and analyze the resultant data. And among all the matching and autosomal triangulations we see, my bet is that very, very few people take the time to compile personal haplotypic pile-up charts and research the chromosomal start and stop loci to identify exonic areas, areas we know contain a significant proportion of protein coding genes (about 20% of the SNPs examined by our current tests are specifically targeting clinically-informing portions of the exome) and exclude or at least de-prioritize those pile-up and coding sections from evaluations.
Ancestry does do that for us, but they won't show us the details under the hood so that we can use their data for our own research and triangulations.
Edited: One little typo between "IBS" and "IBD" makes a big difference. <grumble>
