The ringing of the barrels indicates how securely the ribs are attached to the barrels. The barrels should be tapped at various points up and down the barrels to get a true picture. Cut barrels ring just as well as non-cut barrels so long as the ribs are tight.
The statement about the barrels being the heart of the gun is correct because in order to shot well the barrels must be "true" and flaws in the barrels are much harder to correct (and more expensive to repair) so that the gun shoots well and looks good.
