Yes, the captain has control over the flight, and ultimately the final say. The captain is effectively in charge of the flight; he is responsible for getting the customers from point A to point B. If he feels that he cannot do that safely, calmly, or sees any situation that puts another customer into discomfort or danger, he has the power to act on it.
Most airlines have this policy, if not all. In fact, if this situation would have happened on another carrier, most likely the situation would be a lot more ugly. Southwest is lightyears ahead of many airlines in the customer relations field.
Also, when Mr. Smith bought a ticket, he agrees to the terms and conditions of the flight. That is what is said on Southwest.com or on any ticketless itinerary or confirmation page. One of these terms is that Southwest reserves the right to deny him a seat, FOR ANY REASON. Mr. Smith agreed to these terms and conditions when he bought a ticket. Sure, he probably didn't read them (no surprise there), but he still has to abide by them.
Say what you want about Southwest, but Mr . Smith is probably looking for some attention from his 1.64 million followers on Twitter.
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