GG, it is not a matter of ignorance. How can anyone "know" for sure when the jury is still out there?
As far as I know, the Greek moussaka and the Turkish musakka are different.
Wikipedia confirms this. As for spanakopita, well, I believe it is yet another dish that is named similarly but done in a different way. We do have a dish called ispanakli pide, and the similarity in names alone is a sign that it impossible to determine whether it's Turkish or Greek.
As for baklava itself, I do not know whether it is originally Turkish or not, but again, according to Wikipedia: "The history of baklava is not well-documented; but although it has been claimed by many ethnic groups, the best evidence is that it is of Central Asian Turkic origin, with its current form being developed in the imperial kitchens of the Topkapı Palace."