I have found the following situation bizarre.
NZ leaves from T2 from LAX, where you check in as per usual, show you passort, and give them the above mentioned green paper insert.
You then go through x-ray where nobody asks for a boarding pass/passport, then you board a plane to the uk, pacific, australia or nz.
The problem is that to get on the plane all you need is a boarding pass. There is no-one to stop you changing with some other person who does not not have a visa etc who will then cause all sorts of problems a the other end.
i.e. there is absolutely no gurantee that the person who checked in is the same person using that boarding pass.
Mark
ps. I suppose this is not overly different from two pax "swapping" boarding passes but at least they are both passengers.