Nefrititi lived 3000 years ago and based on her bust wouldn't look out of place in most Mediterranean countries today, there's no reason to think contemporaneous Greeks would look any less Mediterranean.

That's not really true, especially in southern Greece. DNA studies have shown the modern Greek people share around 90% of their ancestry with ancient Minoans and Myceenans. In the South, especially on islands like Crete they're virtually the same. In the North there is some admixture mostly with Slavic and Balkans, and some traces from the Ottoman empire.

Relatively short term occupations or small migrations tend to change an ethnic groups DNA less than you would think. After 4 generations you would end up with the same scenario of seeing the whitest person you have ever seen claiming they're 1/16th Cherokee.