Actually God offered the Israelites the Ten Commandments. Moses came down from Sinai and found them dancing around a golden calf idol.
May be source of the disparity the author is trying to convey.
http://www.chabad.org/parshah/article_cdo/aid/2786/jewish/Underneath-the-Mountain.htm
...The Torah tells us that prior to the revelation at Sinai, the people of Israel “stood beneath the mountain” (Exodus 19:17). How does one stand beneath a mountain? The Talmud interprets this to mean that “G-d held the mountain over them like a jar and said to them: If you accept the Torah, fine; if not, here shall be your grave.”...