Can a human fall 4 miles without a parachute ... and live?

The following incident is related on Wikipedia for St. Nazaire, France:

The U-boat threat to supply convoys across the Atlantic made Saint-Nazaire a constant target of Allied air forces. In the face of determined Luftwaffe fighter opposition to the daylight raids by USAAF Eighth Air Force bombers. On 3 January 1943 Col. Curtis LeMay led 85 Boeing B-17 Flying Fortress's of the 1st Bombardment Wing against the U-Boat pens at Saint-Nazaire, on the Eighth Air Force's sixth raid against the facility. LeMay also introduced the combat box defensive formation, echeloning three-plane elements within a squadron, and squadrons within a group, to concentrate defensive firepower against fighter opposition. Only 76 aircraft found and hit the target, and during the mission seven bombers were shot down and 47 damaged.

The damaged aircraft included the seventh B-17 mission of Staff Sergeant Alan Magee, from which Luftwaffe fighters shot off a section of the right wing causing the aircraft to enter a deadly spin. Wounded ball turret gunner Magee leapt from the plane without a parachute, rapidly losing consciousness due to the altitude. Magee fell over four miles before crashing through the glass roof of the St. Nazaire railway station, which mitigated Magee's impact. Found alive on the floor of the station, Magee was taken prisoner of war and given medical treatment by his captors. He had 28 shrapnel wounds, several broken bones, severe damage to his nose and eye, and lung and kidney damage; and his right arm was nearly severed. Magee was liberated in May 1945 and received the Air Medal for meritorious conduct and the Purple Heart. He was later featured in the Smithsonian Magazine as one of the ten most remarkable survivals of World War II.

I guess at this point the only thing I can add is, "Believe it, or not."