Its more complicated than that. Turkish Kurds (the PKK) would often thake refuge in Iraqi Kurdistan; but with permission (more or less) from the Iraqi Kurds, the Turkish army would enter the zone to attack the PKK.
Actually, the Iraqi Kurds could hardly refuse, dependent as they are on the Turks for their own survival. The US airbases that provide air cover are on Turkish soil, and the trucking routes that are the basis of their economy all go out through Turkish border posts that could be closed at any time. All aid and trade for the region comes through Turkey.
The PKK itself has been quiet lately. Their commander was captured, apparently by US special forces, and handed over to the Turks for trial. He has negotiated a cease fire from his cell, which so far the PKK has honored in hopes of avoiding a death sentence for him.