There is Phrygian admixture in Kurds without a doubt (Balkan affinities are visible in J2b, Ev-13 and I2* levels) but it's more restricted to Northern Kurds. Corduene also known as Gordyene was a vasal state with people speaking an medic_Scythian language and beeing of Gutian origin while worshipping Teshub the Hurrian sky God as well the nature (Old Iranic nature religion) but the name of this vasal State is derived from the Phrygian capital Gordion.
The Phrygian and Urartian admixture is what connects Kurds and Armenians, but contrary to Kurds the Armenians are probably direct descends of the Phrygians.
We need to understand the meaning of Kurd.
Kurd (similar case with Turk) mean originally had this meaning. 1. it was a geographic term describing the mountainous region around Lake Van and mount Cudi modern day "Eastern Anatolia" and North Mesopotamia. 2. It was a synonym for proto Iranic nomad tribes. The Kurti from Lake Van are believed by some scientist to have been either Scythians or some proto_Iranic nomadic group. I even believe that the very name of Balkan Scythians, the Skudra derives from the word Kurd (nomadic warrriors).
The Kurds themselves just recently started to call themselves Kurd, instead when you asked a Kurd in his language what ethnicity he is, he usually asnwered as Kurmanj/Kirmanj (Kur= again association with mountains ?) or Goran, which means herder of the mountains (again association with mountains Gor = Kur? since an is addition to names and tribes in Iranic) or Zoran.
Some people believe that the term Kurd, Kur derive from the Gutians who were also known as described as mountainous people. Some people even believe that the word Kur for mountain in Sumerian was inspired by the ethnic name of the Gutians who came into contact with Sumerians.
My own hypothesis is this. Until now there is no single evidence that the Medes penetrated into Kurdistan from East. Instead there are historical records that they settled in the Zagros mountains coming from West. If there was a migration from the Steppes into Kurdistan than it was likely through the Caucasus. I believe these Kur people in North Kurdistan were the early Gutians and they were identical (the same) as the Kurti of Lake Van. Among some of the names used for Gutians are Qardu, Kardu Karda, Qurti, Kuti, Guti and Kurti probably belongs to this list. They and the Urartians were described as fair featured (compared to the darker haired South Mesopotamians). I even go that far and claim the very name of Urartu is derived from the Kardu form of the Gutians. I believe that the Gutians are those Indo-Iranians of Mitanni who became the Medes when Assyrians captured Mitanni.
Think about it when the Gutians dissapear in the history books, suddenly the Mitanni appear, when Mitanni dissapear suddenly Medes appear. I even have historic confirmation for my hypothesis. Cyrus generally associates the Medes with Gutians. He goes so far and calls all Medes simply Gutians. Heredotus on the other sees the Medes and the early Mitannis as the same people.
