It would be hard to objectively falt the Turks for that. The 'US allied Kurds' did not just want freedom from Saddam's fist, but even after liberation wanted to have a sovereign state of the Kurds that included Kurds from Turkey. No way Turkey, as a sovereign state, would have allowed that ...ally or no ally. It would be like us just sitting back and letting Mexicans take over portions of the SW USA (....hmmm, let's ignore the rather obvious illegal immigration aspect to that LOL) just because our British allies liberated them from some crazy despot. As close as we are to the Brits, we would shoot the Mexicans all the way back.
So, while the US was rebuilding the country, the Kurds wanted more than just a rebuilt Iraq, and their dreams for a Kurdish state extended to parts of Turkey and the Turkish Kurd population. No sane sovereign state would allow that.
The Kurds were split 4 ways during the partition of the Midddle East, and their dreams of a Kurdish state have been set in their minds since. Kurds I met in the 70s informed me that their one goal, one dream was to re-unite their people under one flag in their (Kurdish) land.
I can't blame them either.
The Kurds have been a thorn in many sides, and may yet have that Kurdish State, but in the meantime the pursuit of that long-term goal can cause short-term complications on other fronts.
You are right, in that the Turks could not tolerate the incursions of Kurds who have a different nationality, especially when hostile to Turkish soverignty, but the Kurds see themselves not as Turks nor Iraqis, etc. so much as Kurds, and there's the quandry.