"Inherent accuracy" would have to go to the bolt action, but that doesn't mean single-shots can't be extremely accurate.
I own several single-shots that will shoot right alongside good factory bolt rifles, including several Ruger No. 1's and a Merkel K-1 break-action rifle in .308. My Ruger No. 1B in .22 Hornet is as accurate as any Hornet I've ever seen, and my lightweight .25-06 No. 1 (a Lipsey's special with slim 24" barrel) put 5 shots into an inch, not just 3 shots, with its favorite load two days ago when I was sighting it in.
I also once owned a Browning Low Wall .243 that would put TEN shots inside an inch. It was so accurate I shot the barrel out on prairie dogs. It was deadly out to 450-500 yards.
Single-shot black powder cartridge rifles are also very accurate. I also once owned a Ballard Rifles .45-70 High Wall that would put 5 shots into an inch or so at 100 yards, using a tang aperture sight.
But really, really accurate rifles, those that will basically put all their shots into the same hole at 100 yards, are almost invariably bolt actions. The bolt action is not only stiffer all the way through, thanks both to the action being pretty much in-line with the barrel and the one-piece stock, that the potential for super-fine accuracy is greater, even in factory rifles. These days it's not unusual for factory big game rifles to group into 1/2" or so with the right handloads, sometimes right out of the box, and the accuracy of a custom rifle can be MUCH better than that.
