I think this whole "inherent accuracy" term is something thrown around almost like "which is best" category.
There are, however, certain principles which have helped to define accuracy over the years.
The 30-30 Winchester was considered a great leap forward in its day, when most hunters were using 45 caliber straight walled cases and a lot of them didn't trust that tiny bullet to do what the larger calibers did. But it did establish the concept of a necked down case in America and has been used to great effect for a long time. Most people relate the 30-30 to the various lever action rifles it has been chambered for, and few will claim any great accuracy compared to a properly set up bolt action.
I once had a Savage 340 chambered in 30-30 and while it wasn't a bench rest rifle by any standard, it regularly out shot my friends lever guns. The difference in my mind was the action and bedding of the bolt action itself rather than any superiority in reloading technique. My ace in the hole was that I could use pointed bullets and lose less velocity over distance than their round nose requirement for the magazine.
When the 300 H&H Magnum was introduced, some shooters pounced upon it as "inherently accurate," and it won some medals in competition way back when.
I would guess that a lot of its so-called accuracy was found in its speed, compared to other cartridges. Speed gets you to the target a bit faster, assuming the same bullet, so there is less time for the wind to show effect on the bullet. The idea back then was to use a long, tapered case which was somehow supposed to focus the energy towards the base of the bullet while the pressure built up.
The ballisticians now tell us that a steeply shouldered case keeps the majority of the powder in the case during its burn rather than pushing it down the bore along with the bullet, spreading the burn out. The idea that a short, squat, sharp shouldered case keeps more of the powder located close to the primer for a consistent burn. I think the terms inherent accuracy and consistency get mixed up quite a bit, actually.
The idea here is to use the rifle case as more of a "combustion chamber" and the bullet is the piston. As any builder of high performance gasoline engines will tell you, burning the mixture completely when the piston is near top dead center results in more power and efficiency, while burning fuel after top dead center really doesn't do much more for power as the combustion area is rapidly expanding and the burn becomes less efficient. Engines which have a larger bore than stroke, or "over square" tend to produce more power, especially at high rpm's because you can pack more mixture near the spark plug.
Because the Army did so much experimentation and scientific study on the 30 caliber bullet concerning speed, shape and powders, the 30 caliber was considered an inherently accurate bullet, mainly because there was reportable data on the 30 caliber bullet and all the experimentation done.
Spitzers, various boat tail designs as well as different ogive designs have given us better consistency over distance as we have come to understand the transition from supersonic to subsonic flight of the bullet.
External factors also come into play. The long debate about the 308 Winchester vs the 30-06 being a good one. The 308 has a more efficient "combustion chamber" due to its shape and improved powders. Also, the 308 can be had with a shorter and therefore stiffer receiver action, reducing flex in comparison. Not that you are going to find 2 off the shelf hunting rifles with which to prove that point. That one is going to be more accurate than the other is going to be more of a function of how tight the tolerances are individually than which cartridge one chooses.
Maybe the proper term, especially when it comes to pistol cartridges is how efficient or consistent they are?