The rules say: When both players have the same points, then you determine randomly (e.g. coin toss), who has the initiative. You DON'T determine randomly, who CHOOSES to have or not have the initiative.
By the way: The storecampionship coin is great as a coin toss coin and as an initiative token.
Except when you do, because really, it makes zero difference equalling out to a 50% chance to either have or not have initiative.
I guess I just have a hard time caring, and prefer winning a coin toss to be a benefit rather than "Oh **** I won the toss".
That said, the championship coin is awesome for both initiative and the coin toss.
We've also started using it in campaign. When the coin is on the Rebel side they make decisions and do their turn, when it flips, no changes can be made and the Imperial turn has started, rinse and repeat.
It takes care of those "Wait wait, you haven't activated yet, can I just..." scenarios.