How can the most genetically similar populations to Ashkenazi Jews from an admixture standpoint be Italians, Greeks, Turks, and Armenians?

Question

In this study from 2016, Ashkenazi Jews are shown to be the most similar from an admixture analysis test to populations not traditionally associated with being geographically near Ashkenazi Jews. This study was controversial for essentially stating that Ashkenazi Jews aren't native to the Levant, but that isn't really that related to the question. The abstract to the study states that the analysis of Ashkenazi Jewish genomes "demonstrated that Greeks, Romans, Iranians, and Turks exhibit the highest genetic similarity with AJs". In addition, of the twenty-five populations in the reference population (Greeks and Italians were excluded from said reference population), Ashkenazi Jews are shown to be genetically closest to Turks, followed by Armenians. This data is indeed supported by the admixture graphs shown in the study. What I am essentially wondering is how this is possible. The first is because this study demonstrates that Ashkenazi Jews weren't endogamous at all, contrary to popular opinion, meaning they must have had lots of admixture with Central European and Eastern European populations. The second reason is less scientific, but still a reason nonetheless. While there are indeed many individuals among the populations Ashkenazi Jews are said to be similar to in the study who have a light phenotype, from personal experience (I am Ashkenazi Jewish myself) pretty much all Ashkenazi Jews have a light phenotype, while amongst the populations mentioned in the study as being genetically closest to Ashkenazi Jews, a truly light phenotype is far rarer than amongst Ashkenazi Jews themselves. I feel personally that most Ashkenazi Jews, including myself, look far more like Germans and Poles than like Greeks and Turks. The third reason is that outside of small endogamous ethnic groups, a given ethnic group tends to resemble the peoples surrounding it, which in this case for Ashkenazi Jews would include peoples like Germans and Poles. Ashkenazi Jews are a massive ethnic group with a population estimated at ten million or more people, and as shown above, they were not endogamous. I am not doubting this study's results, but I simply wondering how, given the other information I mentioned, said facts are possible?