Yes, they've always been vague. I suppose that once the Middle East became unofficially and popularly synonim of "Arabic", than those who are not Arabs would not want to be called as such.

Still, if I had to stick to traditional school Gepgraphy, I would have to include Turkey in Middle East, and say that Turkey is geographically Middle Eastern, Culturally not. Or whatever.

Interestingly, while Turkey's political situation is such that they've been repeatedly kept out of the EU (lack of sufficient respect of Human Rights, as well as economic standards not beng met, as well as Greece opposing it fiercely), the few people from Turkey I met seemed completely "western" to me, whatever that means, and I would have not guessted they were from Turkey if they did not tell me.
So, I am not surprised that they don't want to be considered Arabic. They're really not.