To be clear since not really mentioned: The concern is a standard problem of working machines, and machine shops. It is not that metal on metal or plastic on metal or whatever will cause damage, but that there's random junk floating trough the air, on your benches, etc. Often microscopic abrasives. Especially in a smaller shop vs a production facility where you do not separate blasting, sanding, grinding, etc from the cleaning station, there will be abrasives, that can get stuck to the rod and THOSE will wear bits of the barrel you care about.
I've seen it. Old guns (hard to clean from the chamber) with visibly (though slightly) elongated crowns from cleaning, and more. Military armorers see this and more today; overcleaning of all things causes more damage than the dirt. Here's a good example: scraping the carbon off the tail of the bolt of an M16 using the edge of the charging handle. Aluminum on steel, must be safe right? Nope. Causes damage to the bolt tail, whereas the carbon buildup is of no significance at all and can be left there.
For barrels, aside from any level of bore guide to keep it centered: wipe the rod down regularly in use, try to keep it centered, and just generally clean only enough, not vastly too much.