I think they are saying that humans cannot associate palm prints to an individual, unlike face (or even eyes in certain cases). It's just security by obscurity kind of thing but yes, not very convincing argument for privacy.
This is a sleight of hand on Amazon's part. Humans looking at a palm print and identifying the person is not a concern, it's computers looking at a palm, associating it with a credit card, which can then open up a trove of behavioral data to push (i.e., ads) to people. It's disingenuous, like putting someone in a tiger cage and saying "Don't worry, there's no way you can drown in here -- we made sure there's no water."