It's an interesting place to find such a quote, but the idea is pretty uncontroversial. In the early Archaic period (c. 800-650 BC), as mainland Greece slowly reached and then surpassed the demographic and economic standards of the age before the collapse of the Mycenaean palaces, Greek culture was heavily influenced by that of the great centres of civilization at the time. Trade links between growing Greek communities and the thriving, far more highly developed cultures of the East introduced the Greeks to a wide range of inspiring "forms and ideas".

The most famous and obvious of these is of course the alphabet, which the Phoenicians brought to Greece in the 8th century BC. Previous Greek scripts had been syllabic, and had disappeared with the palaces; writing was extinct in Greece for more than 300 years. The introduction of the far more practical Phoenician letters allowed for the renewed spread of writing in old and new forms.

Greek art of this period was heavily influenced by Eastern examples. The typical Greek kouros, or statue of a young man, is derived from Egyptian examples, while most Greek statues at this time had the almond-shaped eyes and mysterious smile typical of Near Eastern sculpture. A whole "orientalising period" is recognised in vase painting, marked by the replacement of old Greek geometric patterns by plant and animal motifs known from the Eastern Mediterranean.

These are very likely to be the "forms and ideas" Nietzsche was referring to, but there are other things as well. Many of the early "discoveries" of Greek science, such as Pythagoras' theorem, were already well known in the East, meaning they were probably not so much "discovered" as learned through increasing contact with more advanced peoples. Unsurprisingly, all the early Greek natural philosophers and a great number of literary pioneers were from Asia Minor - the part of the Greek world most directly connected to Eastern empires such as Lydia and Persia. The trieres or trireme, the warship that became the iconic instrument of later Greek naval empire-building, was a Phoenician design adopted by the Greeks in the later 6th century BC. The earliest coins we know of were found in Ephesos on the coast of Asia Minor, dating to about 600 BC; the Greeks believed currency was a Lydian invention.

In a grave near Argos, dating to the late 8th century BC, archaeologists found this panoply, which is exemplary of the nature of Greek culture at the time. This is the first piece of body armour found in Greece since Mycenaean times - and no part of it is Greek. The helmet is clearly inspired by Assyrian examples. The bell cuirass is derived from body armour known from the Central European Urnfield culture.

In short, when mainland Greece began to grow and expand again after a long period of relative stagnation, it developed a voracious appetite for the achievements and styles of more developed centres of civilization. Early Greek culture certainly did not exist in isolation; a network of trade links and settlements soon connected Old Greece to the far reaches of the Mediterranean, from Spain to Syria and from Egypt to the Black Sea. Whatever they found useful or pretty, they adopted.

An excellent read is Fox's Travelling Heroes, the first part of which goes into detail about trade routes and cultural contacts during the so-called "Dark Ages" in Greece. The author focuses on the trading outposts and routes between Rhodes, Crete, Cilicia, Syria, and Egypt on the one hand, and later Western trade involving Italy, Magna Graecia, Sicily, Africa, and Spain on the other. He emphasizes cross-cultural contact backed by archaeological fact and literary/mythological allusion.

Going back further to the late second millennium, there were numerous trade and high-level political contacts among Hittite, Egyptian, Mycenaean (early Greek), and Levantine peoples. Another good book here is 1177 BC: The Year Civilization Collapsed, which, in tracing the breakdown of this international network, does much to expose its extent.

All in all, the Mediterranean civilizations were much more international and cosmopolitan than many people believe. I think, at least in America, primary and secondary education treat classical and pre-classical history in a very compartmentalized way that gives rise to a false impression of isolationism and lack of long-distance communication. In fact, Fox touches on the compartmentalization a bit since the Greek "Dark Ages" are particularly widely misunderstood. They are Dark because of illiteracy, not a lack of international trade and travel.