I have bought items from AliExpress which somehow arrived from an Amazon warehouse, unexpectedly quickly. The price was right and I have no other complaints, so I think it does happen.
Any fulfilled can use FBA (fulfilled by Amazon) for their own inventory and their own retail front end. Amazon charges storage and shipping fees and the items do not need to be for sale on Amazon.com.
https://sell.amazon.com/fulfillment-by-amazon