It seems likely to me that one of the attractions of Hellenism to Jews during the era of Chanukah might have been the presence of "lost Torah wisdom" contained in Greek Philosophy.
The Maimonides' "Guide for Perplexed" is a work of Judaism styled on an Aristotelian thought template. In Part 2, chapter 11, he explains that these ideas originally belonged Judaism. Due to persecution, the Jews lost touch with these notions, while the Greeks retained them. Therefore, he felt that by digging into Aristotelian philosophy he can reclaim lost Judaism.
Truthfully, Aristotle predates the story of Chanukah. So it's likely that whatever Aristotle had was already lost to Judaism then. The Jews of that era may of had a fuzzy feeling that there was something undefined, yet very familiar in Greek philosophy. Their souls must have heard the voice of Torah ideas calling out to them from a state of exile, like someone hearing the voice of a dearly beloved calling out for rescue from prison.
Truthfully, something like this happens in every generation. The trick is to learn how to distinguish between the prison and the prisoner.
Chag Chanukah Same'ach