So do explain the other "tribes" other than the Cohens who have distinctive DNA strands. This has been proven many times since the study you link to from 2007, a lot has happened in the last 9 years.
What DNA strands are you talking about?
Do you really understand the matter?
Is Judaism not transferred via the maternal line?
Do you know what Mitochondrial DNA (
mtDNA) is?
"The origins of Ashkenazi Jews remain highly controversial. Like Judaism, mitochondrial DNA is passed along the maternal line. Its variation in the Ashkenazim is highly distinctive, with four major and numerous minor founders. However, due to their rarity in the general population, these founders have been difficult to trace to a source. Here we show that all four major founders, ~40% of Ashkenazi mtDNA variation, have ancestry in prehistoric Europe, rather than the Near East or Caucasus. Furthermore, most of the remaining minor founders share a similar deep European ancestry.
Thus the great majority of Ashkenazi maternal lineages were not brought from the Levant, as commonly supposed, nor recruited in the Caucasus, as sometimes suggested, but assimilated within Europe.
These results point to a significant role for the conversion of women in the formation of Ashkenazi communities, and provide the foundation for a detailed reconstruction of Ashkenazi genealogical history".
A substantial prehistoric European ancestry amongst Ashkenazi maternal lineages : Nature Communications : Nature Publishing Group
As we see, all founding mothers of European Jewish communities were European women, who converted to Judaism in the Middle Ages.
So how can somebody who did not inherit their maternal DNA from Sarah claim to return to Israel?
Yes, some Ashkenazi Jews can trance their paternal DNA to the Middle East, but Middle East is a huge region. Palestine is a tiny spot on this map:
https://upload.wikimedia.org/wikipedia/commons/a/ae/Haplogroup_J_(Y-DNA).PNG
So if some Ashkenazi males can trace his origin to the Middle East, then his ancestors may have lived in any of the areas with the high percentage of J-Haplogroups.
What is the explanation?
Well, in the Middle Ages many Semitic merchants traveled from Khazaria to Africa and Asia, some of them converted to Islam, others converted to Judaism, and these J-Haplogroups can be traced by a huge number of people on a huge territory, and most of the carriers of the J-Haplogroup have nothing to do with Judaism.
So if some Ashkenazi and Mizrahi have the same J-Haplogroups, how can this prove that they stem from Hebrews?
Are you kidding?
The conversion to Islam or Judaism does not change your genetic makeup, and the mentioned J-Haplogroup is older than any form of Monotheism.