the aerobic bacteria on the outside of live rock directly feeds the anaerobic bacteria on the inside of live rock.
Directly feeds? You mean it passes it into the rock rather than just releasing it through its cell walls into the water? I am surprised at that. Do the bacteria create little paths through the rock along which nitrates can pass so that the 10-40+x turnover does not just force the nitrates into the water general column?
Do you have any science to back up this statement?
What does the aerobic bacteria on the outside of Bioballs feed?.... right, nothing... boom N-Factory!
But water is still flowing through your tank. If you have live rock (or any other nitrate export facility) and bioballs then the nitrate from the bioballs will get pushed around in the water and dealt with by whatever you use.
The nitrate factory story is just a myth. People noticed higher nitrates when they either:
1) Used only bioballs and did not perfrom regular water changes
2) Used bioballs with live rock and didn't take any care to ensure the bioballs were maintained properly
How many people successfully have zero nitrates when just using live rock on a normally stocked tank? Very few, that is why we have DSB and 'fuges. Bioballs will create nitrates at exactly the same rate as live rock. It is just that if you don't have a nitrate export system they will continue building (or if you let them get bunged up with gunk then more waste is breaking down).
I personally can't see any reasons for a nitrate factory if you design your bioball filtration well (such as a trickle tower which falls into a macroalgae sump).
At the end of the day it is horses for courses. If you want a lightly stocked reef tank where the filtration needs little maintenance then LR is great, but if you want a heavy stocked tank with messy predators then bioballs in a trickle tower will destroy live rock and leave loads more space in the tank for the fish to swim.