However, all Greek charter agreements I've seen will not allow you to take the boat into Turkish waters. I know that TopYacht will charter you a UK owned yacht in Turkey and which you can take into Greek waters. They will arrange all the paperwork for you.
Chartered a boat from Rhodes last year through a Greek company and went over to Turkey for a week. No problem at all. Charter company wasnt bothered and Turkish waters are full of charter boats with a Greek ensign. Send me a pm if you want more info. (You can save sheds of cash if you charter locally)
Nautilus were the UK agents. Greek company was Kiriacoulis, who's Rhodes agent/manager, when asked if we could go to Turkey shrugged his shoulders and said "why not, but I can't think why you would want to". Very droll.