You can change the championship on your brand if you want, I have no issue with that. I just think we'd argue too much if we tried to come to a consensus on who gets the title when, which is why I believe it should be random.
When I say they're on both brands, I'm referring to the previous WWE brand splits when one tag team from another show could challenge on a PPV and take the title to their Brand. I don't know if I'm misinterpreting what you're saying, but what I'm reading is that we're trading off which brand gets the title every month. Maybe I'm wrong.