By virtue of the fact that there was a scrum, it almost means, by definition, you don't have a clear recovery. Think about the Kelce fumble that Gilmore picked up in their game this year. They called it down by contact on the field, but overturned it on replay. The only reason it went to the Pats is because Gilmore is literally the only guy around the ball when he picked it up, which is a "clear recovery."
The reason this rule exists is because when a player is "down by contact" on the field, the whistle blows. Once the whistle blows, guys are trained to stop. So if there's a scrum, or two guys with a shot at the ball, the whistle may cause one of them to not go after the ball. That's why the only way you can overturn a down by contact/fumble ruling is if the defense makes a clear recovery, which more accurately translates to "it was obvious the defender recovered it, and nobody else had a chance..."