The whole story stinks a lot to being an arrangement, or a setup, to make Copenhagen Airport and/or SAS look bad in terms of security.
He also tried to get on other flights in the non-schengen area (but was stopped at the gate) before finally sneaking on to the LAX one.
This is just to pretend, or give the impression, that he/she was confused, and to a certain extend generate confusion on the subsequente investigation.
no record of him being booked for any flights to the US
Of course there were records. There is plenty of time until the flight gets to LA for the 'intelligence comunity' to delete all of those records and achive the above-mentioned outcome. Even to subtract the payed fare from the SAS bank account so as not to leave any loose ties.
The pertinent question is what wants to be achieved by the other side of the pond with this event ? Replace SAS on that route by someone else ?