Confederate batteries generally had whatever they could get their hands on.....much of it obsolescent sweepings from the various Federal Arsenals they appropriated at the start of the war. They produced a copy of the Parrott as well as the Brooke...but not many of either.
It's true that the Confederate ARMY had whatever it could get its hands on, but it was perfectly possible to pool weapons and issue like weapons to batteries. The Union Army did that, the Confederates did not. One consequence of that was that it complicated the Confederate battlefield ammunition resupply problem.