In fact, as Cebrian points out, the Greek tradition of animal warriors and animal heritage stretches far back in time - before the Greeks were ever "Greek" or even lived along the Mediterranean coast. It's a tradition that goes back thousands of years to around 5000 BCE, back when the Greeks ancestors were part of an ancestral tribe we call the Indo-Europeans. The Indo-Europeans were an advanced and powerful nation that lived in the Pontic-Caspian Steppes, just above the Caucuses. They were horse-riders and chariot-builders at a time when most tribes were still wandering on foot and eatin' berries and lame-ass shit.
The Indo-European culture split over time, as all nations do. The first to leave were the Anatolians, who founded the Hittite and Luwian empires in Turkey. Later to leave were the Italo-Faliscans (some of whom became the Italians), the Celts, the Germans, the Indo-Iranians (who further split into the Persian kingdom, the Aryans of India, and many other tribes), the Tocharians (who settled in Western China), the Albanians, the Armenians, and the Balto-Slavs (Russia, Lithuania, Bulgaria, etc...). The Indo-European path forked. Every tribe took its own way and began to innovate and evolve. Over time, each tribe lost parts of its ancestral language and culture, while retaining other parts, so that no single tribe paints a perfect picture of its past.
But much can be recovered.
In the writings and speech of every nation resound the echoes of yesteryear, waiting to be discovered like ancient puzzle pieces and put back together. One of those lost items is the culture surrounding animals and the warrior spirit. The tribes venerated the animals and turned to them as a source of strength.
The Germans revered the wolf and the bear. In fact, the true name of the bear was taboo - never to be uttered. Instead the Germans created a euphemism for its name, which lives on in our languages. English bear, Old Norse björn, and German Bär all come from Proto-Germanic *beron "the brown one." The fearsome Norse berserker was literally "bear-shirter," a mad-man adorned in bearskin. Although the berserker gets all the attention, the more common crazy Norse fighter was the ulfhedinn "wolf-coat." The wolf appears in many of the early Germanic names: Beowulf, Wulfingas, etc...
The Greeks turned to the wolf and the goat. Lykos went on to found the Lykians "the wolf people." Zeus and Athena wear the aegis, the goatskin shield. While Artemis is a goddess over wild beasts, her brother Apollo is master over but one animal, the wolf. All this may point to an earlier tradition of shapeshifting. Berserkers and ulfhedinn probably believed they were becoming the spirit of the bear and the wolf, just as in early Greek tradition, warriors were often depicted in wolf and goat hide. The Saga of the Volsungs describes Sigmund and Sinfjotli putting on wolfskins and being transformed into super-charged wolves. These glimpses into early Germanic and Greek life are windows into their ancestral period, their Indo-European period.
I think it's an exciting possibility and Cebrian's paper is worth a read.
Cebrián, Reyes Bertolín. "Some Greek Evidence for Indo-European Youth Contingents of Shape Shifters". Journal of Indo-European Studies. Vol. 38, Is. 3/4. 2010: 343-357.