I think that Jerry could have done well in the Olympics if he had picked one of the shooting disciplines and trained for it.
The issue is that those disciplines are pretty specialized and need a lot of training that is specifically oriented at the discipline as opposed to just being accessible to a person who is good at some other shooting discipline, or maybe an all around good performer in the shooting sports. Even the Olympic shotgun sports have differences from how they are normally shot in the U.S.
The closest I see to an event that someone might be pretty good at even if they were not specifically training for it is the rapid fire pistol.
In that final round of that sport, the competitor starts with the pistol (a 5 shot semi-auto .22LR with open sights) at low ready (one handed) and at the signal, brings the pistol up and fires at 5 targets set at 25 meters (about 27.3 yards). To score a point, the target (about 4" in diameter) must be hit and the shooter has 4 seconds per string to fire all 5 shots.
The Olympic Gold winner for 2020 was Jean QuiQuampoix who had a score of 34/40 in the final.
A really good bullseye competitor might do pretty well at that sport if they could handle the time constraint and get used to shooting at multiple targets instead of just one.