No, when they get the product shipped in they stick a seller-specific label on it, then commingle it. When I order an Xbox an employee goes to the Xbox bin, picks any of them and scans it out of the system. Amazon now knows which one I got and where it came from, because the barcode identifies it as originating from seller X. If I complain to Amazon or send it back they can now look up what they shipped me and see if some seller consistently ships them bad product.
In essence commingling prevents you from efficiently grabbing something from a specific seller, but it doesn't prevent you from knowing which one you grabbed.
If the unit has an UPC barcode, the unit is commingled (also called "stickerless" inventory). Commingling means Amazon can use one seller's inventory to fulfill another's order - the units are never stored in the same bin to allow tracking origin.
If the unit has an Amazon seller-specific FNSKU barcode, the unit is not commingled.
The used barcode type can be configured by the seller.
The barcode configuration option does not mention commingling at all (but help pages do), so I can understand some sellers getting confused on whether they are affected by commingling or not.
In essence commingling prevents you from efficiently grabbing something from a specific seller, but it doesn't prevent you from knowing which one you grabbed.