High-end shotguns can be as "accurized" as high-end rifles. It's all about perfectly round patterns and short, evenly dispersed shot strings with the correct ammo. But, with any decent shooting shotgun, if your target is in the center of the pattern, you will score a hit. But, it's up to you to put it there.
Rifle and barrel manufacturing has greatly improved in the past 20-odd years. Most rack rifles - excluding some military versions - can hold one MOA or less with the right ammo. If they don't, then that particular rifle has an issue and needs to go back to the manufacturer.
Some rifle competitions rely heavily on shooting skills. But, there are those competitions like bench rest that depend heavily on the rifle, and often become more of a competition to see who has the best hardware.
The bottom line is that in theory, you can have a rifle and ammo combo that can put ten shots in the same hole at 100 yards when shot from a vise. The issue then becomes can you make it do that in your hands. And, if you are a good enough shooter, does it really need to do that for your particular application?
and he made it all the way to the pros (baseball). 
