Why does Verizon say they don’t replace iphone batteries, when other people say they do?

To begin with, it's not possible for you to 'have a new one' for them to put in... Apple doesn't sell batteries. Apple, and anyone authorized to work on iPhones, won't touch your knockoff battery.

Some Verizon locations may be able to replace the battery in your phone. They will NOT do so with a battery that you bring to them, only with a battery supplied to them by Apple.