Unfortunately, the term "direct" is confused with "nonstop." I hear it misconstrued all the time.

A "direct" flight to United can mean one with a connection. UA 106 goes from LAX to ORD then to BOS, same flight number. By the same token, UA 876 goes BKK-NRT-DEN-ORD, hence it's still a "direct flight" since it shares the same flight number on all segments.

Technically, the agent was right when you paid for a direct, but not nonstop flight. Your only recourse is to try another agent who is more sympathetic. But for the future, note DIRECT is not equal to NONSTOP.

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When once you have experienced being a 1K, you will forever fly the friendly skies with your eyes set on 100% mileage bonus and SWUs, for there you have been, and there you will always long to return, every year!