1/2 moa is obtainable with an AR. AR15 and AR10 rifles that have match barrels and match triggers can achieve the 1/2 moa mark fairly easily.
My Armalite AR10 shoots 1/2 moa. With the same twist and length barrel my 5R milspec will shoot .4 moa. So yes the bolt actions are or can be more accurate, but the AR platform is extremely close.
Stag offers a 1/2 moa guarantee on the 6R AR15. Les Bauer, there have been reports of closer to 1/4 inch.
The AR is the exception to the semi auto rule that they can't be as accurate as bolt guns. While I don't think you'll be seeing one win a bench rest competition, they can run with the high end tactical rifles. I suspect the age old idea that a semi isn't accurate comes from the older generation of hunters. A generation where the FN was viewed as how accurate a semi auto is and all sniper accuracy rifles were bolt action. If you wanted a sub moa rifle you had to go to a bolt action or have 10K ready to buy the now prohibited PSG1, the very rare Walther WA2000 etc. The problem is times changed and many weren't interested so they didn't follow the current innovations. What was once sort of true, isn't today.
The design features of the AR rifle done up for accuracy work on the same time honoured accuracy principles seen in many bolt guns. Aluminum stock (the actual receiver), free float barrel, locking rotating bolt, and match grade trigger. The DI does a good job of not creating harmonic and repeatability issues commonly found in piston system semi autos.