The speaker added a twist to the plain meaning of the text: They (the Romans) celebrate an eight-day solstice festival for their own reasons, but we (the Jews) have adopted the practice as a celebration of the Hasmonean victory.ת"ר לפי שראה אדם הראשון יום שמתמעט והולך אמר אוי לי שמא בשביל שסרחתי עולם חשוך בעדי וחוזר לתוהו ובוהו וזו היא מיתה שנקנסה עלי מן השמים עמד וישב ח' ימים בתענית [ובתפלה] כיון שראה תקופת טבת וראה יום שמאריך והולך אמר מנהגו של עולם הוא הלך ועשה שמונה ימים טובים לשנה האחרת עשאן לאלו ולאלו ימים טובים הוא קבעם לשם שמים והם קבעום לשם עבודת כוכביםThe Rabbis taught: when Adam saw that the days were growing shorter, he said, "Oy! Perhaps because I sinned, the world is becoming dark on my account and returning to chaos, and this is the death that was decreed for me by heaven [Gen. 2:17]." He fasted for eight days. When the solstice arrived and he saw that the days were growing longer, he said, "It is simply the way of the world." He went and established eight days of festivity. The following year, he observed both [the eight days preceding the solstace and the eight days following the solstace] as days of festivity. He [Adam] established them for the sake of heaven, but they [the Romans] established them for the sake of pagan worship (B. Avodah Zarah 8a).
Because Jewish holidays are fixed to a lunar calendar adjusted to the solar calendar, Chanukkah always falls around the winter solstace in the northern hemisphere, but it does not always accord with it precisely. Nonetheless, the parallels between Chanukkah and Saturnalia (later celebrated as Christmas and New Year's Day) are clear. Both begin on the twenty-fifth of a mid-winter month and last eight days. The practice of lighting an increasing number of candles on each successive night also has obvious resonance as a solstice ritual.
Could Chanukkah be based on a pre-Roman version of Saturnalia? A Google search indicates that the aforementioned Shabbat speaker was hardly the first to suggest a historical connection between the two. If this is the case, then by calling the holiday the "festival of Sukkot in Kislev" (2 Maccabees 1:9), the Jews of the second temple period were linking a pagan holiday to their own tradition, making it an appropriate context for celebrating the cleansing of the second temple.