There seems to be a lot of misunderstanding about what Y-DNA research is and what it can do. In the absence of Justin (taking a break) Swanstrom I'll try to explain it from my relatively lay information.
Y-DNA is DNA from the Y (male) chromosome. It mutates relatively slowly (on the approximate order of one step, or less, per century - some bits have a somewhat higher mutation rate). Due to its origin it can only be passed down directly from father to son(s).
Various factors can interfere with this transmission: no sons; adoptions, formal or informal; name changes for legal or prestige reasons; and, infamously, "the milkman".
It is possible to triangulate a *probable* descent by finding that several well-documented male descendants all have closely matching patterns. The more descendants tested and the closer the matches, the more probable the descent is. One can never *quite* rule out the chance that a more recent ancestor who is *not* of the line is being fingered instead - as in the notorious case of Richard III vs. the five Somerset descendants (an attempt, actually, to define "Plantagenet Y-DNA", since the common ancestor was Edward III). This one is especially instructive because on one side (Richard's) there was a recovery of actual ancestral Y-DNA. On paper they all should have matched - but *none* of the Somersets matched Richard, and one of the Somersets didn't even match the other four (thus proving that a rumor about his relatively recent ancestry had some basis in fact).
The most that Y-DNA was able to show in that case was that four Somersets had as their common ancestor Henry Somerset, 5th Duke of Beaufort (16 October 1744 - 11 October 1803).
There is *somewhat* greater likelihood that Richard III's haplotype G is "the real Plantagenet", rather than the four Somersets' type R1b - the descent chain is longer on the Somerset side, with a recent "cuckoo in the nest" and two known non-marital transmissions (starting with John of Gaunt's own sons by Katherine Swynford). But it is by no means a certainty, and the only thing that would clinch the case for one side or the other would be matching ancestral Y-DNA - of which there is a profound scarcity (no good looking for John of Gaunt, his tomb and everything in it got burned up in the Great Fire of London).
Another way a joker can get into the deck is when the "ancestral DNA" isn't from the person you were looking for. A recent attempt to pin down the Y-DNA of the Dukes of Normandy went aground because the bodies in the tombs dated from *too* long ago - somebody, at some time, had been playing "shell and pea" with the ancestral remains. (It is suspected that something along those lines explains how the "Bourbon Y-DNA" turned out to be haplotype R, per descendant testing, instead of the supposedly "proven by ancestral Y-DNA" haplotype G.)
In this connection it has to be said that while we know the Bourbon haplotype with a high degree of certainty, we can't be sure that it's the same as the Capet-Valois haplotype. Henri IV, first of the Bourbon kings, was only a 9th cousin to the last of the Valois (lots of room for something to go funky there).
If it is eventually found that "Grey of Rothersfield Greys" doesn't match Grey of Codnor, Ruthin, Wilton, etc., you can put the blame squarely on Hawise de Grey, sister of Bishop John de Grey of Norwich and mother of Archbishop (of York) Walter de Grey and Sir Robert de Grey of Rothersfield. *Hawise* was the Grey in that line, and if her husband wasn't a Grey cousin (possible, but at this point purely hypothetical), then he adopted her name because he was "lower on the totem pole", and the "Rothersfield" haplotype is actually his, whoever he was.
In some cases it is possible to say that "John James Smith" belongs to the family of "James William Smith", but because at least one step in the paper trail is missing, it may never be possible to know exactly *how* they are related - an especially difficult problem if "James William Smith" had a lot of sons and/or his sons had a lot of sons.