We've got two heavy-barrel Savages in the family. A Model 10 and a 111. Both shoot well under MOA with good ammo. I'd classify both of them as half-inch rifles. Savage "lead the charge" on factory accuracy ten years ago and they've built a reputation as accurate rifles. Some say that they're ugly and Savage has heard that criticism and worked on it. A couple of years ago, they moved the cocking indicator/bolt release from the right side of the receiver to a button near the trigger guard. They've also become very innovative in listening to the market and trying to give shooters the rifles that they want.
I don't believe that you can get a more accurate rifle right out of the box than a new Savage. However, the other companies have been paying attention and are putting more focus on factory accuracy. It's getting hard to find an inaccurate factory rifle. The market demands it and the companies are responding. I believe that we live in a golden age of rifle manufacturing. We're seeing factory rifles come out with a built-in MOA potential, something that was unheard of 40 years ago in a factory rifle.