I hear this all the time. I think this is a rumor created by someone who has never actually brined an pre-injected bird, and who is speaking theoretically. I've been brining pre-injected birds for 20 years. Use the regular brine recipe and brine for the recommended time. It will not be too salty. The amount of salt that is injected is not that much, and equilibrium with your brine will prevent it from being overly salty.