All Turks know that; all Iraqies, and Syrians, and Iranians, and Assyrians --- all know that. Which is why the Turks are so nervous. They are also afraid that we may loose control over the Kurds and the latter will move to establish the state contrary to our demands (this may still happen; do you think we will start shhooting at the Kurds? Turks are right to be very, very nervous).
This is just one of those rooms with an antrance and no (nice) exit that history has built.
Basques are in a very similar position. Considered to be decendents of the original Iberians ("people of the river"), who lived on that land even before the Celts invaded the peninsular, they have not been concured by anybody --- not even Romans. THey have their own language, live on their own land concurred by all sorts of foreigners, and this land is even contiguous. Should they become an independent state, in which case France and Spain should give up that land? Go back to a_Turk's reply, and you'll understand better the refernce to the Basques.
The same is with the our Southwest. Surely it was not always ours. What do you do if it wants to "return" to that previous state.
Whatever you decide on these matters, it up to you of course. But you should not through around your accusations and withdraw amity from the Turks so easily: no number of Armenian and Turkish friends qualifies us to do so. Look more deeply into the problem. Things are much more complex. As I said earlier, history leads you into certain rooms from which no suitable exit exists.