Now. Much more interesting is your point about using DNA to identify the mother of John West as a Pamunkey "princess".
I haven't seen the evidence, but I would be very skeptical. DNA could certainly support an oral or written tradition, but it's hard to imagine a scenario like this one where DNA could prove descent from a specific person.
That's not to say there aren't other scenarios where DNA can pinpoint an ancestor. For example, if a mutation can be shown by triangulation to have originated with a particular "recent" person, it's not much of a stretch to suppose everyone who shares that mutation is a descendant. I want to emphasize the word "recent" because it is not possible ever to rule out completely the possibility of the same mutation appearing independently more than once.
My guess about this Pamunkey princess is that someone has done some triangulation here. The link in the profile goes to a dead page but the description of it says the data is from a study by the National Park Service. I would still be skeptical.
It's fairly easy to envision a scenario where yDNA, mtDNA, and autosomal DNA of various descendants converge in a way that proves a Native American descent. Perhaps it is just somewhere in this area of the tree. Perhaps they have data to pinpoint the mother of John West. No way to know without reading it.
And, if they have found evidence of Native American DNA in this line, it is not much of stretch to think they could be drawing on historical context to say it is likely Pamunkey. In general there are not sufficient data to link specific DNA markers to specific tribes, but we would have to know whether there are any yDNA and mtDNA lines that are thought to have been linked to the Pamunkey. I haven't heard of any, and I probably would have, but I'm not so dogmatic as to think I've heard everything worth hearing ;)
So, in the end, my short answer to this question would be that I can see how someone might think they've made this kind of connection but I'd want to read the data and analysis for myself.