I made an language error, too. While my comment about zero-value crowd-source reporting is valid, the real exacerbating issue at more distant cousinships is a corollary, that the "crowd" will seldom report a relationship where no DNA match has been reported by the testing/comparison companies: you don't know what you don't know. For example, last year AncestryDNA changed its matching threshold from 6cM to 8cM. Similarly, FTDNA recently stopped showing very small segments, no doubt because those small segments in the chromosome browser confused more people than they helped...and it conserves CPU cycles.
As the relationships become more distant and the expected sharing amounts decrease, the closer those amounts move nearer the reporting companies' minimum thresholds, and the more the crowd-sourced values can greatly skew the ranges.
I have less faith than you do in the average contributor to the crowd sourced information. Some comments from a few years ago here. With the low-end of the centiMorgan ranges being underreported by the very nature of the beast, even a single in-error value at the ridiculously high end will distort the data. In his data summary, Blaine himself said that he manually caught and removed obvious errors in contributions like the longest segment showing a greater cM value than the total amount of sharing reported; that some submitted relationship descriptions were indecipherable; that there were instances of text and no numerals being entered for cM values; that he had at least one submission indicating a 7cM total sharing for a parent/child relationship. He also writes, "Some relationships were almost certainly entered incorrectly, which might be due to misunderstandings of 'removed' relationships in genealogy. Other relationship errors were clearly due to misattributed parentage events resulting in the believed relationship being incorrect."
So, no. Pareto's law: only about 20% of the people using DNA for genealogy will have more than a rudimentary knowledge of it. The Shared cM Project is open to anyone for contributions--I've provided upwards of 50 entries myself--but no one has to show bona fides to indicate they know what they're doing. And a single contributor who mistakes a 2C1R for a 4C is making an error on the order of an 800% magnitude.
Too, any evaluation of cousinship distance based on DNA ultimately comes down to probabilities. Probabilities can't be estimated unless some baseline or benchmark has been established. So in that regard I'd say that every question about autosomal DNA sharing amounts involves some median, average, baseline, or benchmark. We can't really avoid it. Hyperbole, but until the 1950s, the Rapa Nui peoples of Easter Island were the most endogamous society on earth; they were simply too isolated geographically to have a diverse genetic pool. That all began to change with commercial air travel, but prior to that if a single Rapa Nui had shown a verifiable 4th cousin relationship that displayed 140cM of DNA sharing due to generations upon generations of pedigree collapse, that wouldn't be of useful or practical value as a benchmark for anywhere else among the world's 7.8 billion people. Is such a result possible? Sure enough. But the odds in the general population would be astronomically, and I'll bet a Benjamin Franklin that you could split Blaine's histogram for Grouping #9 right down the middle of the chart, throw out everything on the right-hand side, and arrive a more realistic value range.
AncestryDNA uses a hybrid approach to relationship estimation once the segment processing has gone through BEAGLE and Timber. They use both actual data derived from "thousands of pairs of individuals with known family relationships," but they rely more heavily on a common bioinformatics process of generating vast numbers of simulated individuals with controlled pedigrees in order to see what the distributions are like. For this they use the catchy term "in silico," meaning experimentation performed computationally (i.e., using silicon chips) as opposed to in vitro or in vivo. 
They incorporate no pedigree collapse into the modeling: all pairs of individuals in the simulations share exactly two ancestors or no ancestors. From those data they define IBD (identical by descent) intervals that correspond to the maximum-probability relationship estimates; they use full cousinship levels only, no half or 1x removed.
There are additional steps after that to better ensure that closer relatives (with greater than 90cM shared) aren't impacted by computational phasing errors from the BEAGLE procedure, and to evaluate "IBD2," or places where segments are shared on both sides of the family (essentially FIR matches in addition to HIR). The number of shared segments in addition to the amount of sharing also factors in (but at the level of 5C and beyond more than a singleton shared segment is unusual). The graph they present in their white paper, which is intended to be only an example, goes only as far as nine meioses, or birth events, equivalent to a 3C1R, and shows a range of 40-75cM, but they note that only IBD greater than or equal to 40cM is displayed. A step above that--at 8 meioses, or equivalent to 3rd cousins and Blaine's Grouping #7--the range shown is 75-90cM (my extrapolation of Blaine's data there shows, at a 68% CI, a min/max of 29/115, so pretty close).
Beyond a general description of the process and those broad ranges, I don't believe that AncestryDNA provides any additional insight into their actual data and operations.
