Bottom line is the barrel being the biggest contributor to accuracy potential. Bedding and shimming are both important as well, but all the bedding and shimming won't help a crappy barrel.
I have to respectfully disagree given that this is talking about the M1A/M305/M14 rifle.
The best barrel in the world will do nothing if the rest of THIS rifle is not tightened up first.
This is no AR style free floating barrel, lazy man's bolt action rifle. There is so much slop in the system that can easily cause changes in barrel harmonics. Hell, it can easily change POA!
We know how critical a barrel is to maximizing performance in bolt action rifles but the assumption here is that the rest of the rifle is not flopping around like a dying salmon.
As for chamber being the root of accuracy, NEVER is - as long as it is cut true to the bore, it can be made to work. The bore itself and the stability of the barrel metal is what separates good from great.
The relationship of the bullet to the throat/leade has a bigger impact on accuracy then the chamber. The chamber is just the combustion area. The rest of the barrel takes care of the precision.
Note: not discussing the issues from the extractor groove back.
Most military barrels are far from consistent bore/land dimensions over its length. They may not be drilled true and are rarely stress relieved. Produced with the eye for low cost, high speed and long wear, bug hole accuracy is more a fluke then anything.
I would say of the M305's I tuned, not one shot worse then 1.5 moa at 200yds with most hovering in the MOA range (handloads of course). That was factory barrels, and bolts (I do not like USGI swaps and especially no 60's bent up op rod spring), using an affordable 2 screw scope base, shimmed gas system, and tuned orig trigger.
There is little doubt such a tuned rig with a Kreiger barrel should shoot that much better. However, we get to the land of diminishing returns where the platform becomes the biggest variable.
I have yet to meet an aftermarket stock that would do anything better then the orig style properly bedded. In fact, those that try and free float the barrel without other serious changes to the action, usually shoot worse.
YMMV.
Jerry