Originally Posted by Majuki

This used to be true but now isn't. There was an arrangement where if you were a US Passport holder with Global Entry registration you could use SmartGate (automated passport control). SmartGate is now open to all US Passport holders (and a number of other nationalities as well) with an ePassport. I believe New Zealand still has an expedited lane for those US Passport holders with Global Entry, but you have to have the Global Entry card in hand to use that lane.

This isn't a catch all because of course you can have Global Entry (as a permanent resident or via an arrangement with your country's government) but not have a US Passport.