Hi, Valerie. The absolutely crucial point is one you described: "assuming the test-takers' trees are accurate." I admin a few FTDNA projects, and that's always the bottom line: the paper trail. Unless there's the opportunity to directly analyze remains--for most of us, slim to none--we're always left with trying to figure out who is actually descended from whom.
With yDNA, since there is no recombination during meiosis in the majority of the chromosome, the part we compare, people familiar with using autosomal DNA can sometimes be confused by the term "genetic distance" as applied to yDNA. Results on the Y chromosome can't be predictive of relationships in the same way that autosomal DNA can, so "genetic distance" has no direct correlation to the number of generations separating individuals; instead it references simply the number of assumed, independent mutation events that have taken place based on the STR (simple tandem repeat) counts.
Looking at the Sargent DNA Project, I gather that it's Lineage 01 and Lineage 05 that we're talking about. FTDNA switched several years ago from a purely stepwise count of STRs to what's called the infinite allele model; all that really means is that some variation counts, particularly in STRs that display multiple values (like DYS459, DYS464, YCAII, etc.), are given a little slack because more than one change might have occurred in a single generation.
A quick and admittedly cursory look at the modal values for Lineage 01 and Lineage 05 show me a genetic distance of 15 at 37 markers. FTDNA considers anything beyond 4 a non-match at that level, and I believe even that is lenient. In my Williams subproject, we have multiple men who are a genetic distance of 4 at 37 markers who we know, based on the full sequencing of the Big Y test, cannot be related until circa 900-1000 AD. In other cases, a GD of 4 at 37 markers might apply to men who are separated by 10 or 12 generations from their MRCA. But a genetic distance of 15 is considered a non-match if even 111 markers are being evaluated.
It looks as if no one in either Lineage 01 or Lineage 05 has taken the Big Y test, so the basis for analysis is limited. But it's extremely likely that the common ancestor between those groups would date back thousands of years; no biological relationship at all within the genealogical timeframe.