Who's they?
The airline.
They sold a ticket. That's a contract, and THEY ought to honor it.
They should be treated as a private enterprise and a private enterprise should retain the right to refuse to do business with any other private enterprise or individual. They would, of course, have to return any funds received for the services not rendered.
Reasonable. Quite reasonable. That is, if it was indeed the airline that refused to let the ticketed passenger board.
But then it would be reasonable also for the airline to compensate the denied passenger for any acutal economic loss as well as hardship and inconvenience for the airline's unilateral abrogation of a contract.