No I disagree I think the West Asia admixture varies, in the Near East/West Asia it's significantly higher than Southern Europe, Greco Anatolian admixture in Europe is 10 to 15 percent, in Near East I mean the average Near Easterner it's close 20 to 25 West Asian to percent this is a map of Indo European heritage.
In West Asia, the chances of anyone of Indo European heritage is less than 20 percent, those plots are a bit off.
However, I do agree that a so called ''West Asian'' person has wholly European genetics it is within the spectrum of the East Mediterranean it's because Neolithic Indo Europeans were Southern/South East European in genetics. The West Asian Greco Anatolian input will
never vary in Europe as much as it does in West Asia
https://en.wikipedia.org/wiki/Prehistory_of_Southeastern_Europe