For a modern Turk to claim that his ancestors fought at Troy is like a modern Englishman claiming that his ancestors built the Stonehenge. Sure, he may be partly descended from someone who was living there at the time, but the great majority of his ancestors from that time were more than likely living in a different part of Europe (or Asia) altogether.
In the same way, I think it is lame for modern Greeks to take credit for the achievements of an ancient community which has long been gone.
As it has been discussed in many threads with other fellow Turks, the Anatolian Turks are descendants of previous populations of Anatolia including IE (Hittite, Luwians, Pala, Lydians) and Non IE Anatolians (Hatti, Urartu), Greeks, Phrygians, Assyrians, Armenians, Persians and so on. Only 10% maybe (based on DNA) descend from Altaic populations.
The point I made though in this thread is that the populations of Anatolia were not Turkic/Altaic nor did they identify themselves as Turks. In the case of Troy, its citizens were most probably Luwians who had no knowledge of Turks and probably referred to Greek speaking people as Ahhiyawa.
As for England and Stonehedge, it is another story. I saw a documentary where they found the immediate modern descendant of some cave people living in Britain back in 4500 B.C. However, Britains population was probably not large which makes the Brits largely descendants of Indoeuropean people who came to the Island after the building of Stonehedge. Regardless the DNA material of each region, the Stonehedge people did not identify themselves as English.
I know your concern about macros statements, but I wanted to make clear that genetically, Turks of Turkey are not unrelated to the previous inhabitants. As an ethnic identity (Turkic) and culture (Turkic & local
of medieval times) of course, it is another story.
As for Greeks, it is an everyday thing nowadays to detach the achievements of the past and focus on how to achieve things today. Achievements of the past are just good for story telling and common historical memory. Your everyday life depends largely on what you do today. Nor Plato nor Solon can help us now.