Nope, we did it last year. Got to the border at Ipsala, all they asked for was the car documents. He entered those onto his computer, stamped Fi's passport with a little car stamp (the car is in Fi's name) and off we went. Coming back in they just checked the computer, overstamped the passport and we were back. There are several people that we know have traveled in and out without needing a carnet. One person we know even asked the Customs Police in Fethiye if he needed a Carnet, the reply was "why? it is your car you can take it anywhere you like" Friends went through Edirne at the same time as we went through Ipsala last year, they had a couple of hours hassle with the Turkish Customs Officer until they complained to the boss. He showed the official a paragraph in an official book, the Customs Officer read it and then said OK and stamped their passport and off they went.
Our take on it is that as a Turkish citizen needs a permit to leave the country it stands to reason that if they want to leave in their own car it needs a permit too, which is the Carnet (a temp export license) We foreigners can come and go as we please so therefore our Turkish car can go with us. As usual the officials who need to carry out laws or regulations don't know them.
So, no problems last year either for us or for friends and we will be doing the same this year.