> Grey market is buying a companies items (not counterfeit copies) outside of the official supply chain. For example, many goods are sold cheaper in other markets. So someone could buy the item there and bring them to a market where they are usually sold for more and be able to undercut the the official supplier's prices. This is perfectly legal thanks to the First Sale Doctrine.
You're mixing up a bunch of ideas. The traditional definition of "grey market" is buying an item oversees at a low cost and then importing it into the US. For example, the identical textbook usually sells for much more in the U.S. than it does in Asia. The supreme court has indeed ruled that the First Sale doctrine allows people to buy that book in Asia, then sell it back to someone in the U.S. for more.
However, the first sale doctrine only applies to copyright, not patents. It hasn't yet been decided as to patents.
More meaningfully though, the meaning of the term "grey market" has expanded. It used to refer to authorized items sold overseas, but now it more generally refers to items with questionable IP rights. When Amazon is using the term "grey market", they are referring to counterfeits and infringing products as well.