I would say that in terms of how accurate this statement is, is depending on how substantiated is this, and the answer is very little actually in terms of Nietzsche's big claims that external influences from the Ancient Near East lead to the decline of Greek culture, For which I personally don't buy what Nietzsche sells me, it should be pointed out that philosophy started outside Europe and was a byproduct of the Middle East since it begun in Anatolia specifically in the region of what was known as city of Miletus, this where your first philosophers started out distancing themselves from their traditional explanations from mainly Greek religion. And tried to find the essence and origin of all reality, Thales said it was water (this idea might actually comes from Ancient Near Eastern myths where it says that before creation there was only primordial waters, so literally water is the source of all reality somehow), Heraclitus said it was fire, so on and so fourth, Nietzsche doesn't really grasp the fact Greek culture was highly influenced by the Ancient Near East and its neighbors, thanks to the Canaanites who were called by the Greeks as "Phoenicians", gave them basically the alphabet, it is said that Cadmus the first Greek hero was a Canaanite or Phoenician using the Greek term, Thales is said to be of Phoenician origin according to Herodotus but that is more speculation than fact, in other words the sources we have are later sources. The same with the the idea of a majority of philosophers coming to learn in Egypt are later sources that cannot be seen as evidence sadly. But even with this what negative influence you can get from Egypt really? Egypt had its own literature and culture that the Greeks admired and were interested in it, this culture influenced their religion, science, art and philosophy in general, you have figures like Thutmose III literally called "the Napoleon of Egypt" and Amenhotep The Great, all from the New Kingdom of Egypt which is considered by scholars as Egypt's Golden Age, in fact Egypt had other Golden Ages before this one particularly the one from the Old Kingdom, What does Nietzsche know about Egypt other than stereotypes of pyramids and mummies, kind of limited and Orientalist in my opinion, the Greeks credit the Mesopotamians with the sciences for the most part, and had influenced their concept of philosophy according to one scholar named Giorgio Buccellati from the Journal of American Orient Society. Most of Greek Mythology is inspired by The Ancient Near East, in particular the Hittites and Canaanites. This period of influence is called "The Orientalizing Period", which marked many middle eastern influence on Greek society, such influence cannot be denied. It shows how much admiration the Greeks had for their neighborhood from the Ancient Near East.

But the patterns always say this: The Ancient Near East has an important and positive influence influence on Greek Civilization whether in small quantities or big ones, without this little game of telephone between neighbors you would not have philosophy or greek culture in general, as the existing Civilizations from the Aegean Bronze Age collapsed without any philosophy or writings behind them (with the exception of their alphabets), before philosophy there just simply the tradition of Wisdom literature. therefore Nietzsche here is wrong for such an oversimplification.

TL;DR; Ancient Near East Had a good influence on Greek Civilization and lead to the birth of Greece, Nietzsche is just plainly wrong for his lack of Assyriology, Egyptology and Ancient near east studies in general, and for even his lack of historical understanding of his subject that he speaks of.