The Constitution is silent on the issue (never mind what machinations the SC has to go through to come up with something), so the government has no authority to allow or disallow it. The Constitution does not grant rights (or privileges) to the people. It grants authority in limited areas for the government to intercede in the affairs of citizens.
That was not the impression I got from his post. As you point out, the government doesn't have the constitutional authority to grant flying commercial airlines as either a right or a privilege.
Flying is a privilege, granted by the owner of the carrier.
People who purchase airline tickets are dealing with a commercial enterprise, not a government entity
The airlines should have the right to deny service to anyone who violates the terms of purchase of their ticket, but CAIR is chipping away at this