Talk about, "Old women's tales," as we are prone to call the more weirder stories that have gone the rounds of yore, "Breaking in a new barrel," by a system of shoot, clean, shoot clean, every shot, oops, every third shot, should be on the top of the list!
No one will ever convince me this is any different than just shooting the damn thing and give it normal cleaning. If you are a competitive bench rest shooter you likely will have your new barrel lapped before you shoot it, but most everyone else just shoots it. After a time it will be more polished than it was when it came out of the factory, but whether this improves accuracy is highly debatable. The bigger worry seems to be how much can it be shot before it starts to lose its gilt edge accuracy.
If you want to improve the accuracy of your new rifle it is of far greater importance to have it properly bedded.
OK guys, have your fun!