If I started using FBA and supplying an item, it’ll go in the same box and chances are more likely an “sold by amazon.com” will sell my product, and I’ll sell an “amazon.com” product.
See the problem?
No they don't. Google 'random stow' and you'll find articles about how Amazon stores incoming items. They are stowed somewhat randomly, but scanned as they are stowed. So the system knows where to find each unit again, and can use that to optimize picking paths.
I was commenting only because most people make the same false assumption (that all units of X in warehouse Y are stored together) and find the random stow model interesting when told about it.
You are referring to mingled inventory which the seller has to opt into explicitly when they decide how to sell their product.
This is not the default, and in my experience, very few sellers choose this option. Most of the inventory is labeled with Amazon-proprietary bar codes that identify the seller.