I'm not saying it's easy for everyone - but for some people it may be that easy if that's what's pushing their daily sugar/calories over a certain limit. I guess that's if you believe that weight gain/loss has anything to do with calories which is a
separate topic covered in a few
spots 
My money is on the fact that by cutting out all the extra sugar/salt that he wasn't as hungry and didn't eat as much here and there in small enough ways that's hard to notice. In effect that's still linked to the soda but not as directly. Then again we tend to look at nutrition and weight as a system where one effects the other.