This is only my own opinion, but I think that everything points to that Turkey backed off because they were forced to. Davitoglou and Erdogan are too trigger happy and anxious to start a war against Syria, so therefore I genuinly think that there were two other players that made an offer that Turkey couldn't resist.
First of all we have Iran massing forces on the Turkish boarder. Iran by itself is already a big headache, but Iran combined with the prospect of joining forces with the Kurds would definitely be be a game changer. With 20 million Kurds living in Turkey only, they would be able to conquest lan and hold on to it while Al Quds and the Republican guard make deep incursions. Basically, the whole South-Eastern Turkey would be lost as the most powerful weapon would be used against them, meaning demography. As an occupation force, you need to be so much stronger than your enemy and you need to be able to control things on the ground, down to a street level. An occupation force dealing in an hostile environment would be easy prey to lightly armed guerilla fighters iand with Iranian backing, the Turks would not have the manpower to hold on to the territory. Put this against a motivated Kurdish population that would be willing to throw everything behind.
Overlooking the whole mess, we have the Russians. They have been unnormally quiet during the whole period, which leads me to think that they are more than prepared to act if either Syria or Iran are threatened. Mark my words, they will defend Syria if it comes to a foreign intervention as we then will have a clearly defined adversary. Rebels fighting the Syrian government is one helluva task to reverse as we are talking about a popular uprising and assymetrical warfare. On the other hand, having a foreign power invading Syria, then you know what to hit and where to hit in order to create as much damage as possible. If you take a look at the map, Turkey is practically defenseless against Russia and if Russia takes out Turkish air defenses, which are quite poor in the Northern parts, the country will be wide open for both tactical and strategic bombing. Turkey is just over the pond witn no NATO countries in between. Also, it doesn't take more than one tactical strike and all political capital of Daffy Duck and his friend is lost. The Turkish government is extremely sensitive to any setbacks, while Syrians and Iranians are fighting for their existense and can go all in as they have nothing to loose. As for Russia, they might give the death blow to the Turkish government from distance with almost no risk at all.
As I said, Russia don't dare to loose neither Syria nor Iran and especially not through foreign intervention. They are currently rebuilding their super power status and what is at stake is Russia's ability to protect their allies. If Russia were to loose in this game, they would most surely loose its allies in Central Asia. Heck, even Lukashenko and Belarus might even turn on Russia and start to look westwards in order to repair the damage with EU.