Originally Posted by NM
The requirement varies by country. For the USA, if you do not have residency status, it is the carrying airline's responsibility to ensure you have the right permission and documentation that is required for entry into the USA.
Exactly. And, as with everything else, different agents will check more carefully than others. I flew to the USA with UA once with several waitlisted return dates. Got there with no problems. While there, I flew to the UK. UA at LHR would not let me leave without giving me a confirmed booking for my return to Australia, even though UA in Australia had let it happen!