I would say the idea that Lee "retreating without harassment" is inaccurate. The Union cavalry doggedly pursued him, but Stuart's cavalry did a good job holding them off.
I think the idea that Gettysburg was a turning point is derived from three things.
1. It was Lee's first real defeat with the Army of North Virginia.
2. Lincoln's famous speech at Gettysburg brought extra importance and attention to the battle.
3. Of all the battles of the war, Gettysburg is the one most What If'd by The Lost Cost. What if Stuart wasn't away? What if Stonewall Jackson was still alive? What if Ewell had attacked Cemetery Hill? What if Longstreet had been prompt and obedient? What if the bombardment had been more effective? And then there's the mythologizied High Water Mark. The Lost Cause narrative defined the popular understanding of the war for a long time and thus raised Gettysburg to preeminent status.
Modern scholarship (the last 40-50 years has definitely turned away from the idea that Gettysburg was the turning point, perhaps even a turning point, of the war. Studies have compared how Confederate soldiers wrote about Gettysburg in the late summer of 1863 vs how they wrote about Vicksburg, and the evidence is clear the latter had greater impact on Confederate morale.
I think there was also a study that indicated Chancellorsville was more devastating to the Confederate army than Gettysburg because the quantity and quality of officers lost.
In terms of winning the war, Lee certainly hoped the achieve a dramatic victory against the Army of the Potomac, but this was as motivated as much by the frustrations of Fredericksburg and Chancellorsville as anything. There's also a substantial logistical element to the campaign (see Kent Masterson Brown's book for a good study of the subject). Antietam was before the Emancipation Proclamation, shortly before Union midterms, on the heels of Lee seemingly driving McClellan from the gates of Richmond then winning a dramatic victory at Second Manassas over Pope, simultaneous to the Kentucky Campaign. Antietam was a much greater turning point than Gettysburg: stopping Confederate momentum, influencing elections and government policy.
Jeffrey William Hunt's recent works show how much the Army of Northern Virginia recovered its numerical strength within a few months after Gettysburg and how Lee was still able to launch an offensive to throw Meade back toward Washington (Bristoe Campaign). Lee was also above to vigorously block Meade's offensive maneuvers that fall, even after detaching Longstreet.
The Overland Campaign in 1864 doesn't play out like it did because of Gettysburg in 1863, but rather because of Grant and his dogged determination to keep the initiative - the very thing Lee had tried to do through most of 1862.
In summary, I would say if I had to pick one turning point of the war it's Antietam, but if I could pick multiple turning points I would say:
1. Antietam
2. Vicksburg (for obvious reasons)
3. Chattanooga
- squanders the Confederate victory at Chickamauga
- was the last chance for the Confederates to win in the Western Theater; from this point forward the numbers are overwhelming
- replaces Bragg with Johnston, and places Hood in the Army of Tennessee
- elevates Grant to General-in-Chief
4. Overland Campaign: takes the initiative from Lee, never to be regained, and forces the ANV into a position where they are slowly ground down to ineffectiveness
Bringing the