What rights are being denied? A private company running a private plane is providing you transportation. You don't have ANY rights there. Hell, even under normal circumstances, you could buy a ticket and end up in an overflow situation and the Airline decides who makes it in.

This general argument only makes sense when there is vibrant market competition. Otherwise, it is just couching authoritarianism in some illusion of choice. There is little difference between a bona fide government and a corporation that has become so entrenched that people are forced to interact with them. Especially when the entrenched companies cooperate to set industry wide policies.

The OP answers this question in excruciating detail.