I maintain that Genesis 3 records not only the fall of man but also simultaneously the fall of Lucifer. Satan's fall is his temptation of Adam and Eve. Called to serve mankind, this high-ranking angel chooses instead to seduce mankind to serve him. This seems to me to make the most sense of the record. Everything was very good at the end of the 6th day of creation. Then on the seventh day we have the fall of Satan and Adam intertwined.
The angel Satan, who was created with the rest of the angels to serve man (Heb. 1:14), rebelled against his God-given role in creation and become man's tempter. That was the fall of Satan. The judgment in Genesis 3 against Satan is God's judgment against his original sin. Genesis 3, therefore, documents the fall of Satan and man.
Consider also Christ's comment in John 8:44 regarding Satan: "He was murderer from the beginning, and does not stand in the truth, because there is no truth in him. When he speaks a lie, he speaks on his own, for he is a liar and the father of it." Satan is Satan in virtue of his dual role as the first "murderer" and as the "father of lies." Where do we see him do these things? At the temptation of Adam and Eve. It is an attempt to bring death upon mankind (murder) by means of a lie. Just the opposite of the purpose for which he, as an angel, was created.
The idea that Satan fell sometime before Adam and Eve’s fall originated with the Church Father Origen in the 2nd Century AD. Origen, then, seems to be the primary source for the "standard, accepted view" of the fall of Satan. Origen places the fall of Satan and his angels prior to the creation of the world, motivated by pride directed against God (De Principiis 1.5.5, 1.8.3; Homilies on Numbers 12; Homilies on Ezekiel 9.2; Commentary on Luke 30.2; Gregory of Nyssa seems to have followed Origen here (see A.J. Philippou, "The Doctrine of Evil in St. Gregory of Nyssa" in Studia Patristica: 9:251-256). This same version of the story is repeated by St. Augustine of Hippo from which it becomes the standard view in the Latin west (On the Free Choice of the Will, Book 3; City of God 11.10, 13, 15; 14.27; Commentary on Genesis 3.10, 11.13-30). Augustine is, of course, followed by most other Latin writers (St. Anselm of Canterbury, St. Thomas Aquinas, etc.).
This is one of those times that tradition got it wrong, I believe. It make so much more sense to read Genesis 3 as the record of the original sin of Satan and the fall of man.