The barrel will always point to the same spot when at rest between shots, if it is properly mounted in the action and the stock is not giving it variable tenstion.
The problem/solution comes in the barrel vibrations as the bullet is zooming towards the muzzle. A curious and fortunate thing happens with .303 Enfields, for example--slower rounds exit the muzzle when it's vibrating more "up" than do the faster rounds. In their world of 2-3 MOA, they found that accuracy actually improved a bit somewhere beyond 600 yards. Turns out the trajectories of the faster and slower rounds were converging at that magical distance, whatever it was.
The Browning BOSS improves accuracy by letting you adjust the barrel vibrations so they are consistent for each shot, _for the moment the bullet leaves the muzzle._
Although you would expect the barrel to vibrate exactly the same way for every shot, all the other variables (including those shot-to-shot velocity and pressure differences, maybe?) leave us with some LOADS spitting the bullet out when the barrel is in the middle of either whipping up or down or sideways or whatever.
Bedding becomes very important if the action is able to SHIFT tiny bits in the stock during bullet travel. All the repeatability of your barrel and sights/scope and all that goes out the window if the entire action is being "bumped" around between primer ignition and bullet exit.
Hope this helps...