Ackley tested that 'cord wear' myth back in the 30's. He tied two cleaning cords together and looped the whole thing through the bore of a rifle, and then around the wheel of an electric motor. He turned it on and started looking for evidence of wear, especially where the cord was pulled tight against the crown and the chamber throat. He left it running for days, without detectable wear. At one point he added assorted metal grit from his workshop floor, since that's supposed to be one of the culprits that 'destroy barrels', and left it running for days. No detectable wear. Not a scratch.
Yes under extremely high pressure and continuous use (edge of a knife, earthmoving equipment, snowplow blade) softer materials can wear harder materials.
Running a brass or bronze brush and an aluminum rod through the hard chrome-lined bore of your rifle has 0% chance of 'ruining' that barrel. I just don't believe it.