All of the human race share about 99% of the same DNA - a large amount of our DNA is common to bacteria and many ancient organisms and these studies are talking about the differences in the other 1% or less. Also most of these studies are talking about mitochondrial DNA, which is inherited from the mother. This form of DNA persists unchanged for millenia and has been used to track population movements etc, but it only tells you half the story or less.
Although there will be remnants of the male side of your family going back many generations and these will have a very significant effect on your general physical and other features etc, it is much harder to study or trace.
The 2015 study above said that the Orkney islands had the most distinctively different DNA in the UK and what that really means was that in the small subset they studied - very few if any women with genes common elsewhere were part of the study sanple. Wales was the next most distinctive part of the UK in terms of genes with no markers for Anglo Saxon genes in any of their sample.
We know there was significant migration from England in the nineteenth century to the industrialised Welsh valleys, but overwhelmingly this would have been men migrating - the amount of women migrating would have been lower, so there will be very few markers for what might be thought of as non-preexisting DNA.
Its very complicated and people make sweeping statements sometimes which don't really stack up.
My DNA would probably show up as very typical of other people in Wales, since all my maternal lines were all from Wales going back as far as can be traced, but I'm proud that I have Great Great Grandfathers on both sides who were immigrants, but very little of their DNA will be detectable now even though I might strike a starting resemblance to one of them and to many very distant relatives in England who have never been to Wales.
What I'm trying to get at is that you could be a spitting image of one of your Welsh ancestors on the male side, but even the best of scientists would be very hard pushed to identify the genes or markers that code for it