Does cleaning with and pulling back through the barrel a copper- phosphorus brush destroy the crown of the barrel?
I have heard that it will cause minor scratches to the crown and diminish accuracy

Yeah Right!

How the heck else are you going to do it?

Don't worry about it.

It would take a lot of brushing to made any noticeable difference to the crown.
Most match rifles will wear out a throat a lot quicker than they will a crown.
That will also depend on how well the user of the brush understands how to properly use it. When pulling the brush back into the bore over the crown edge, it should be pulled in slowly giving it a chance to self center thereby not wearing the bottom of the crown. Good luck

In theory you should push the brush through, but not pull it back past the muzzle. I always do pull it back through and suspect the vast majority of shooters do also. I haven't ruined a crown yet, but I guess I'm still working on it. Best wishes.

Cal - Montreal

Going in both directions is ok, just do it carefully. However, by all means, use a cleaning rod guide. They replace the bolt and allow cleaning rod entry from behind the action. They will prevent you from pulling all that crap back into the action.
If you are truly worried about harming the crown, push the brush all the way through and then unscrew it and carefully pull the empty rod back out of the bore.

For cleaning in the field, I FINALLY ponied up and bought Boresnakes. They clean great and there is little chance of damaging the crown as you pull them through.

I will continue use cleaning rods for maximum cleaning, but the 'snakes work great and they can be used when the rifle is still warm and the gunk hasn't hardened.

A benchrest guy at the range told me to use one-piece rods made out of carbon fiber or steel. Aluminum (and brass to some degree) inbed pieces of carbon and then the rods work like a file on the bore. Makes sense.

If you use multi-piece steel rods they should be pulled through as the seams can damage the crown if pushed. The guy and his rifles shoot better than I do. I tend to listen to guys with that much experience and expensive equipment.

Your arm will fall off long before you damage a crown if you use some common sense...

Boresnakes work good. I think as long as you keep the your rods clean and use a rod guide your bore, crown and throut will be fine. I like coated rods myself. Every time they are run throu the bore I clean them with a patch. Good luck, 338vt

The "damaging the crown" is BS!!! I once saw a man start with a 26" barrel at matches, matches were every 2 weeks, and he cut off 1" of barrel AND DIDN'T RECROWN and each match for 6 matches.........HE WON!!!!! EVERY MATCH!!!! He cut the barrel with a saw!!!!! Crown damage is myth of the gun rag writers!!!!! Can crown damage occur? YES!!! But not in the proportion to which the rag writers typify!!!! voo-doo press!!!! GHD

Last year Saeed performed an extensive test in damage to crowns. Check the forums.