I have a .308 that will do 0.5 MoA "all day." Unfortunately, there are few days that I am good enough to make it work to that level. Also, what i've found that greatly affects the accuracy repeatability is the concentrcity of the ammunition. I've gaged a number of factory "target" ammunition and a lot of it has highly variable round-to-round concentricity. This type of variability has a huge affect on highly accurate rifles.
If I'm using the rifle in a situation where high accuracy is imperative - I go through every round with a concentricity gage and tweak the bullets in the case until the round-to-round variation is under 0.001 - and you can see the difference in accuracy.
That's what I find so interesting about precision rifles and shooting - figuring out all of interactions in the entire system from the load and bullet type to the actual physical configuration of the finished round.