I don't see where is the conflict between both things I said. I said I can buy the flight on the same LY ticket, but marketed as AA67, and I asked home come the same flight, marketed as LY8127 is zeroed out.
Some people prefer to purchase the flight under LY code. The code under which a certain flight is marketed doesn't change the protected - I'll be protected if it's on the same ticket, and otherwise not. It doesn't matter under whose code the flight is.