For the OP: As you can see, cleaning and care of firearms is like religion... everyone has one, everyone thinks theirs is the one and only 'true' method, etc. No offense meant, but benchrest shooters are like NHL goalies. More superstitions than you can think of, and you'll never convince one of them to admit they may not be right. So leave them be, whatever keeps you happy and shooting is what matters.
99.99999999% of the damage done to rifle barrels through cleaning them is done through careless cleaning and/or with the multiple-piece rods. Especially the super-cheap aluminum rods that pick up and hold metal filings. This includes cleaning from the muzzle end.
For heavens' sake, clean your rifle. I've seen many good rifles ruined through NOT cleaning them (pretty heartbreaking to look down the bore of a once-accurate Parker-Hale in .270 to see a fuzz-filled (rust) tube because someone forgot to clean it after hunting season). Leaving primer and powder residue sitting in the bore is asking moisture to collect and do its dirty work.
No Boresnake is going to abrade any barrel, ever. Neither will a bronze brush. They are both softer than ordnance steel. Particles left in it through NOT cleaning the Boresnake as others have mentioned might. Free advice, take it or leave it.
Get a one-piece rod, Dewey or Tipton, and the appropriate jags/bronze brushes, and a bore guide, and a good cleaning cradle. Get a Boresnake, use it for one pass after each shooting session with that rifle, and clean the Boresnake. Do a thorough cleaning with the rod/guide combo at the end of your shooting season, or at least once a year. Keep the barrel lightly oiled and the action even MORE lightly oiled (just bought a 597 VTR from a bubba who thought oil seeping out of the seams was a good thing), and that rifle will outlive you.
Hopping off the soapbox.