Turkey did not accept partitions because it pissed off Russia, Turkey did not really care for Poland it was simply to annoy its political rival
No. Turks always respected Poland and its fighting ability, and even though you're partially right, that they we're not on friendly terms with Russia at the time, they also did it to give the Poles some of their dignity and honor back. You have to remember that the Turks we're no small power at the time either, and they backed up their words to a degree. A lot of Poles escaped to Turkey and formed their own communities, and a high ranking General, Jozef Bem even became governor of Aleppo. Countries always look after their own interests first, thats how its always been. But Turkey could have just as easily remained neutral and kept Poles out of their country.
It makes you wonder - what would have happened if Poland and Turkey allied themselves? Now that would have been a potential powerhouse.
I still think Polands greatest blunder was going to the aid of the Austrians at Vienna. Sobieski should have kept his troops away from this, and let Austria and even Germany get overrun by the Turks. The Turks would have been stretching themselves quite far after that kind of advance, and would not have likely turned their sights on Poland and Eastern Europe. At least, not for a while. Poland-Lithuania could have allied themselves with them and formed a great commonwealth of three countries.
The Austrians were so grateful that in a 100 years they would be carving up Poland for themselves. Goes to show that you should look after your own ass FIRST, always.