It all depends on what you mean by the word "sniper."
If you by sniper you mean a highly-trained precision marksman skilled in land nav and fieldcraft whose mission is to gather intelligence, observe the enemy, and engage high-value targets at ranges starting around 600 yards and extending out to over 1000 yards, while operating in two-man teams, then bolt action is the way to go, with the spotter toting some sort of semi-auto.
That is the current configuration of the Marine Scout-Sniper. That there would be why the word "scout" is part of the job description, and even listed first.
However, if by "sniper" you mean the old Soviet doctrine, or the current US military "Designated Marksman" concept, then you are talking about a slightly-more trained marksman whose job it is to be part of a rifle platoon and to deliver accurate rifle fire on targets at slightly longer ranges than standard rifles and standard riflemen can reach, then a semi-auto that is accurized, but not actually "precision" is the way to go.
And yes, you can, if you spend a whole lot of money, get an M14 to the "precision" level of shooting.
No, shooting one "MOA" at 100 yards is not really precision. I have an accurzied Rem 700 in .308 that has shot more than one .25 MOA groups at 100 yards. I have hit steel silhouette targets up to 1000 yards away with regularity at a pair of courses at Badlands Tactical with this beauty.
And no, the accurized M14 just won't stand up to the rigors of actual field use and abuse, without constant tweaking and retouching by highly-trained armorers with the correct tools.
There's been talk that AR-10 type rifles can be tuned to real "precision" standards, but I don't know about lots of data showing that tuned AR-10s can maintain that level under realistic field use and abuse conditions.
But again, it all depends on what you really mean when you use the word "Sniper."
Do you mean the scout-sniper model? Do you mean the designated marksman model?
And yes, sometimes, such as in the recent book by the Marine sniper who took part in Operation Iraqi Freedom, scout-snipers get employed as designated marksmen, depending on the specific situation.
hillbilly