Some claim that running bronze brushes through the bore can do damage to the rifling.
I can hardly believe this because bronze is much softer that the steel a barrel is made of.

Who can comment on this?

Lies.

Might not be the bronze brush, but improper use of the cleaning rod--without a boreguide, or without wiping it down to get the accumulated crud off it before the next series of strokes. Or, cleaning from the muzzle rather than from the breech.