In the book "Jewish History in Conflict""Jewish History in Conflict", Mitchel First compiled and categorized many of the Jewish responses to the discrepancy between the Seder Olam and secular dating. It would seem that at least some maintain that disregarding the Jewish dates conflicts with belief in the Torah:
ה' יצילנו מדעת החיצונים כילדי נכרים יספיקו המוסיפים הרבה במנין מלכי פרס ומאריכים שנותיהם מאד ולא ימצאו ידיהם ורגליהם בבית המדרש כי בהכרח יצטרכו להכחיש גם המקראות - May G-d save us from the view of those outsiders, who "please themselves in the children of strangers" (Isaiah 2:6Isaiah 2:6), who add many to the number of Persian kings and increase their years greatly. They do not know their way in Jewish learning because they will necessarily be forced to contradict the biblical verses as well... (Rabbi Yaakov Emden, commentary on Seder Olam pg. 88)
(The author notes that R' Emden does not specify which verses he is referring to which contradict the secular dating, but writes that he probably was referring to Daniel 11:2Daniel 11:2).