If you accept the DNA results then the DNA data show that:
A. The lines of John III and Samuel theOrphan (Walkers Creek lines) share a common ancestor
B, All three of the lines in the Natural Bridge Grouping share a common ancestor
C. The Natural Bridge and Walkers Creek lines do not share a common ancestor.
The question that many will be concerned with is "which of the two lines descend from John I", because they both can not if you accept the YDNA data
We have primary data that connects at least one of the Natural Bridge lines to Goochland County. We have primary data that connects the line of John III to the Nottingham Lots.
If you believe that John II and Katherine Rutherford lived on the Nottingham Lots, and are buried in the cemetery at Rising Sun, then you might conclude that this is consistent with John II being the father of John III. Its not consistent with the available primary data for the Natural Bridge line because:
1) we have no primary data that connects anyone in that line to the Nottingham Lots, 2) We have data that connects this line to Goochland County.
There are reasons to wonder if John II and Katherine lived and were buried in the Nottingham Lots. Not good reasons, I think, but I could make a case that this couple came from elsewhere, and that someone as yet unrecognized as John II's parents were on the Nottingham Lots.
The preponderance of evidence, however, seems to work best if you accept that John II and Katherine settled on the Nottingham Lots, and that they were the parents of John III and Samuel. Since we do not have DNA evidence for others in this line (Gunstocker John and his brother Alexander, and James who married Mary Guffy) we're just guessing about their connections. But we know that Samuel the Orphan lived on Walkers Creek, and that John III owned land there
(at least briefly). I presume that they are in fact related to the other Walkers who lived on Walkers Creek, at least initially. Some of the Natural Bridge line did come to live there, but that was after the two lines intermarried.
There are many ways to interpret the data, and we doubtless do not yet have a clear picture of what's going on. But if you accept the YDNA evidence as it is currently understood, you can not accept that the family history as presented in White 1902 represents a single family. Rather, you are forced to conclude that she merged two (or perhaps more) families.
I think you have to keep an open mind on this, and its possible that some problem may be discovered in the future with our interpretation of the YDNA data. However, for now, we've got two separate lines, united in White 1902. White 1902, by the way, is not the one responsible for this merger. I believe she did the best that could be done with the information she received. There are tell-tales in the non-DNA data that point to a problem of some sort, but White can't really be blamed for misunderstanding the family tree. I believe that the family had already merged the two lines well before the mid-19th century. White just used their data, and assumed they knew what they were talking about.