Yeah, that's part of it. But it's a valid consideration, after all, since Turkey (not withstanding it's recent, and self destructive, failure of will and foresight wrt the Iraq War) has been one of our most stalwart allies in the Muslim world for many decades.
It would, even more significantly, risk destabilizing Turkey and thereby potentially collapsing the only Muslim democracy in the region (and just about the only one period in addition to Indonesia). At the same time it might also destabilize Iran and Syria (which also have large Kurdish minorities) but, OTOH, since these countries are already despotic it might also provide pretext for continued or increased oppression.
More generally, and most gravely IMHO, the creation of an independent Kurdistan could lead to independence movements on the part of other ethnic minorities in the region. This sort of thing has typically, and to put it mildly, NOT been a good thing. See, for instance, The Balkans, WWI, WWII, Rwanda, etc.
Again, on general terms, although the record is certainly mixed, I think that (supra-ethnic, nation-state) nationalism has mostly been a positive force in the Middle East, as a counter to both ethnic strife on the one hand, and pan-Arab nationalism or pan-Islamism on the other. This is especially true in the Arab world since the modern nation-state is a secular institution, whereas alternative polities, including ethnically based super-states, are often not.
Finally, it is important to maintain the territorial integrity of Iraq and its neighbors because of the fact that, in consultation with Turkey and other states, the international community, Iraqi expatriate groups, and etc, we committed ourselves to this principle prior to the war. American credibility, constancy and commitment to its promises widely doubted in the region. We cannot afford to reverse ourselves on a basic commitment such as this one.
According to this article, the Kurds are no threat to them.
Ralph Peters does not quite say that. He says that Iraqi Kurds are (broadly speaking) ready to engage in a good faith effort to cooperate with other ethnic groups in the creation of a new, democratic Iraq (with the expectation, I might add, that they will have some local autonomy under a federal type system).
Peters himself does not advocate an independent Kurdistan, so far as I know, and says nothing in this article about Turkey. In recent historical fact the Kurds in Turkey fought a bitter terror war against the Turks, replete with numerous mass casualty bombing attacks against civilians. This went on for some 30 years until the Turkish army defeated the militant Kurds in their own mountain strongholds and captured their leadership.
Granted that the Iraqi Kurds were mostly or reluctant wrt supporting the Kurdish guerrillas in Turkey (or absorbed with their own woes) but to blithely claim that the Kurds are "no threat" to Turkey flies in the face of the last three decades of history.