One response to Rav Schechter's point is to be found in the writings of Rav Dovid Tzvi Hoffman:

The Sages did not permit their investigations into creation to be made public, but since science has revealed all the results of its own investigations to everyone - results that are likely to shake faith in the truth of Scripture - we are obligated to bring the hints of the Sages to light... In many places, and especially in the book of the Zohar, it is proven that the expression "day," as it appears in the account of Creation, is not to be understood as an ordinary human day of 24 hours, but rather the intent is to the day of God, which lasts 1000 years - that is to say, a day that lasts for an undefined length of time. (Rabbi Dovid Tzvi Hoffman, Commentary to Genesis, p. 48)