I have never heard of a 1/4 MOA M14. Some high dolar match rifles will shoot 1/2 MOA groups at times but not consistently. A more realistic goal is 3/4 MOA for your high $ M1A.
Take a look at the high speed footage of this M1A match rifle. Note how the parts of the rifle move, how parts shift, how the action moves in the stock. In a perfectly tuned match rifle, consistent accuracy comes from the parts consistently returning to their previous position after each shot.
http://www.youtube.com/watch?v=fFmVrfhBzHg
3/4 MOA is more than enough for head shots up to 400m and center mass up to 600m for a competent marksman with the M21 and M25 sniper rifles.