Shutoku Shia,
I don't believe that one particular make of gun is absolutely more accurate than another. Remingtons have always shot great for me and I'm sure there are others who will say the same for Winchester, Sako or Savage. The heart of a rifle's accuracy begins with its barrel and absent a good barrel, everything else is just bells and whistles. A good scope, rings and base (or iron sights), set-trigger, glass (or steel) bedding, match chamber with handloaded ammunition is all for naught when the barrel is pure junk.
The issue then is which factory makes the better "factory" barrel. Better for what? A bullet for X grain and shape or Y grain and shape? Hunting or target? My point is that there are many things which the factory can't control. Type of ammunition (commercial and the quality or handload and the quality?), maintenance or care, one piece coated cleaing rod used, chamber guide for rod, jagged tip for patch or "two-way" patch holder, type and quality of brush all affect how long a barrel holds up. How about the quality of the shooter or even an Olympic grade shooter on a bad hair day? These are factors clearly outside of factory control which will affect the longevity and accuracy of a barrel. Factory barrels, like the features of an action, are designs which are influenced by the compromises the engineering, production and other departments have agreed upon and as you've guessed, some makers make better compromises than others.
Unless you go to a custom gun maker, factory barrels will lean towards the maximum end of SAAMI specs (to ensure the safety of the shooter). Mind you, this doesn't make for the best match chamber. Also, the twist the factory puts on the barrel may not be the optimal for the type of bullet you want to shoot (OK, so this is putting the cart before the horse) and twists, in my opinon, are selected for a broad range of bullets the consumer will be putting through the barrel.
While I've enjoyed great shooting with my Remingtons with their factory barrels, this does not preclude Winchesters from delivering just as small of a group. Lest we forget, Carlos Hathcock used a Winchester M70 on his first tour (86 confirmed - though a few of these may have been with the 50 caliber Ma Deuce) and a Remington 700 on his second.
For further reading, I recommend Harold Vaughn's book, Rifle Accuracy Facts. It's great reading but for me, raises more issues than it resolves (which I hope will result in more research for a Vol II).
Gary