Oh my God, you clearly didn't understand my point. Let me make it simpler:
Totally undivided PIE (Anatolian+all other branches): 3,500-4,500 BCE
Earliest attested IE-derived languages from Hittites, Mycenaeans, Mitanni etc.: ~1,600-1300 BCE
Chronological difference: ~1,900-3,200 years
Undivided Proto-Turkic: ~500 BCE - 1 CE
Modern Turkic speakers: ~2000 CE
Chronological difference: ~2,000-2,500 years
Is it clearer now? Did modern Turks come straight from the Proto-Turkic homeland and are direct, unmixed, immediate descendants of the early speakers of Proto-Turkic in that very far homeland? No, they aren't. The same thing almost certainly is true for PIE speakers and their descendants many centuries, even millennia later. Your reasoning is very weak from a historical and linguistic point of view.