Not exactly. In order to claim someone is selling a different item, it probably goes without saying that the products actually have to be different.
Another seller using their own FNSKU doesn't mean anything by itself. All the FNSKU does is help Amazon keep track of which units of inventory were sent in by which seller. In other words, assume you and another seller are both selling the Webkinz Pup in the post example. Inventory from you and another seller might be exactly the same, but different FNSKU's help Amazon know which units of inventory came from you and which came from the other seller.
However, this is only true for sellers that have elected to the disable Stickerless Commingled setting from their account. If both you and the other seller have enabled Stickerless Commingled, Amazon won't differentiate between the inventory that was sent in.
Conversely, disabling Stickerless Commingled ensures that your inventory won't get mixed up with that of another seller. So, for us as private sellers, this is important if you want to purchase something from a hijacker to ensure that they don't have an genuine copy of your product. If it's different, you can then contact Amazon to try and get the removed from the listing.
I know this is really confusing, so I hope the response made sense. Let me know if anything isn't clear.