For a discussion on real, honest accuracy see
http://www.chuckhawks.com/practical_accuracy.htm I was VERY happy that, shot at 100 yards from sandbags, my Weatherby Vanguard in 300 Wby Magnum did an honest repeatable 1.75 inches with little load workup of hunting rounds.
The best military (type) rifle accuracy I've been able to find is an American Rifleman machine rest test of the new SIG 516 in 5.56x45. Its best performance was with 69 grain match ammo that resulted in 5 shot groups of from .89 to 1.42 inches at 100 yards, an average of 1.12 inches. Top of the line bolt action sporting rifles get from about 3/4 to 1.5 inches, depending on the ammunition, in these NRA tests and its not reasonable to expect an old, mass produced milsurp to do anywhere near as good.
As for the ammunition, according to Hatcher's Notebook the 30 cal match ammunition produced for the US Army usually had calculated dispersions of .3 inches, and about .5 inches when shot from test barrels. But the specifications for normal military ammunition production were:
Cal. .30 M2 Ball
500 yards test - Mean group 13 inches (2.6 MOA) Maximum group 38 inches (7.6 MOA)
With the vagaries of normal military production and a real military rifle barrel a high degree of accuracy seems impossible and a requirement of 3 MOA - and I assume spec match type ammo had to be used so any inaccuracy wouldn't be blamed on the ammunition - seems reasonable.
I didn't feel like buying an M14 Milspec, but below is some sourced information from a Wikipedia article on sniper rifles - 1 minute of angle (MOA) is roughly 1 inch at 100 yards. These are dedicated sniper rifles. Milspec accuracy requirements range from 3 MOA for most main battle rifles in western nations to 6 MOA for the combloc Ak types. Note that these are maximums and any rifle that doesn't test within them supposedly would not be accepted.
Wikipedia:
In 1982 a U.S. Army draft requirement for a Sniper Weapon System was: "The System will: (6) Have an accuracy of no more than 0.75 MOA (0.2 mrad) for a 5-shot group at 1,500 meters when fired from a supported, non-benchrest position".[6] Actual Sniper Weapon System (M24) adopted in 1988 has stated maximum effective range of 800 meters and a maximum allowed average mean radius (AMR) of 1.9 inches at 300 yards from a machine rest, what corresponds to a 1.6 MOA (0.5 mrad) extreme spread for a 5-shot group when using 7.62 x 51 mm M118 Special Ball cartridges.[7][8][9]
A 2008 United States military market survey for a Precision Sniper Rifle (PSR) calls for 1 MOA (0.3 mrad) extreme vertical spread for all shots in a 5-round group fired at targets at 300, 600, 900, 1,200 and 1,500 meters.[10][11] In 2009 a United States Special Operations Command market survey calls for 1 MOA (0.3 mrad) extreme vertical spread for all shots in a 10-round group fired at targets at 300, 600, 900, 1,200 and 1,500 meters.[12][13]
In 2008 the US military adopted the M110 Semi-Automatic Sniper System which has corresponding maximum allowed extreme spread of 1.8 MOA (0.5 mrad) for a 5-shot group on 300 feet, using M118LR ammunition or equivalent.[7][8][14] In 2010 maximum bullet dispersion requirement for M24 .300 Winchester Magnum corresponds[7][8] 1.4 MOA extreme spread for 5 shot group on 100 meters [15].