Oh, there are a LOT more reasons than that, and it doesn't take any access to classified intel reports to see them.
The Peshmerga isn't going to fight for anything that isn't ethnic Kurdish territory, and expecting any kind of decisive results from some combination of the Iraqi Army and the Free Syrian Army is just ludicrous.
Relying on the Free Syrian Army in particular has to be making Putin's day, now he knows he can **** with us the way we ****ed with the Soviets in Afghanistan, trickling in some special operators and equipment to his nominal ally, Assad, to burn up all the resources we want to waste on the FSA.