Does Psalm 3 tell the story of Absalom's rebellion?

The title names the occasion: "A Psalm by David, when he fled from Absalom his son" (3:1). The story itself is told in 2 Samuel 15 to 18, from "The hearts of the men of Israel are after Absalom" (2 Samuel 15:13) to David's grief at the news of Absalom's death (2 Samuel 18:33). The psalm doesn't retell it. Apart from the title, the psalm names no person but the LORD and God: not Absalom, and not any of the adversaries, the "many" (3:1-2). It doesn't say who said "There is no help for him in God" (3:2), or where the psalmist lay down (3:5). These notes set the title beside 2 Samuel as the texts stand, and don't fill in the psalm's lines from the story, or say when the title was written.