In this process Amazon, Walmart fulfill orders, provide customer & return service on sellers’ behalf. For that you have to ship your inventory to their warehouse. You can buy Brand name inventory from Supplier or Distributor and get it shipped to their warehouse.
FBA or WFS can only be done for Private Label: No it's not, you can also sell someone else brand or a big brand name like NIKE, SONY as FBA & WFS. FBA & WFS is just a process of doing business on Amazon and Walmart.