Another question would be the reliability of bolt actions. I've been reading that bolt actions are pretty much as reliable as they come. But in order to achieve accuracy, do they also have tight tolerances that you have to clean them all the time?
The bolt action system is pretty much the most reliable rifle system in the world. The super-duper benchrest match rifles do have tight tolerances, but the usually never see dirt or battlefields so reliability doesn't really matter. The Accuracy International Arctic Warfare (AWM) rifle as example (which is issued to many special sniper units all around the world) has an ice-groove in the bolt, if the bolt is frozen shut the ice groove helps to break the ice when rotating the bolt. The groove also collects dirt, oil etc. and keeps the action clean.
Take a look at the older bolt action rifles, I'm sure you know the Mosin-Nagant 91/30? That was the main battle rifle of the Soviets in WW2 - Sloppy bolt, very loose tolerances so it could function in the Russian climate in snow, mud and ice.
Though the sniper variants of this rifle (just an ordinary rifle + scope and modified bolt handle) could archive MOA or one inch at 100yds and with the 3x magnification PU scope sharpshooters killed enemies out to 500yds.
With the right ammo pretty much all modern bolt actions are capable of MOA and even sub-moa accuracy, even a short barreled hunting rifle with a thin barrel, MOA is pretty much THE standard all modern bolt action rifles have to meet. If an off-shelf bolt action rifle doesn't shoot MOA its junk and should be returned to the dealer.
What makes the bolt action rifle so accurate? Its a very accurate design because it has very few moving parts, the receiver and bolt are very stiff, and most importantly its a simple design, there is not much that can negatively affect its accuracy .
Inaccuracy of semi-automatic rifles is mainly caused by the moving parts and complexity which negatively effects the harmony of the rifle when fired, another factor is the reloading system, with a gas piston you need a gas block on the barrel which also affects the barrels harmony when firing, the barrel is not free-floating anymore. Also, the reloading system - the gas notch bleeds of some gas to power the piston that operates the bolt, the piston starts to move before the projectile has completely left the barrel, the moving piston can also cause slight variation in point of impact. If something moves in the rifle it also moves the rifle itself.
And lets not forget the bolt, some rifles like the FN-FAL have a tilting bolt and not the tightest tolerances in the world, the bolt goes down in a notch and locks up, the upward pressure from a fully loaded magazine on the bolt can cause some variation in point of impact because it changes the angle of the bolt face and thus the angle of the cartridge in the chamber. Inconsistency, the biggest enemy of accuracy.
In a nutshell: a simple design is inherently more accurate, there are less factors that can negatively affect accuracy.
A single shot bolt action rifle is pretty much the most accurate system in the world, and thats why bench rest shooters use this system.
Anyway, I also forgot about this rifle that I had written off, just because I wasn't feeling much love towards bolt action, or traditional rifle stock when I first saw this rifle:
Don't write them off, bolt action rifles are awesome, they are built like tanks, extremely reliable and pretty much indestructible. In fact, my SHTF rifle is a bolt action rifle because a SHTF rifle must work under the worst conditions imaginable, can't do that with a semi.