DOT rules and laws aside, the real document to pay attention to is the "contract of carriage"
All airlines have this, and when you buy any plane ticket, you basically have to live or die by it. United's, for example, is a 37,000-word legal document that, in its 30 very-detailed rules for flying, stipulates that United retains rights to certain passenger personal data, various liabilities, and -- the big one here -- "Rule 21: Refusal of Transport." Under that rule United is thoroughly within its rights to remove you if...
- you're barefoot
- you're naked
- you smell (unless you qualify as disabled)
- you're intoxicated or so high on drugs that you endanger other passengers
- you can't sit in a single seat with the seat belt buckled and the armrests down
- you are 9 months pregnant (unless you provide a doctor's note less than 72 hours old at time of flight saying you're fit)
- you're "both blind and deaf, unless such passenger is able to communicate with representatives of UA by either physical, mechanical, electronic, or other means"
If all of this sounds like a bit much, it's totally totally legal and standardized. (It also includes stuff like concealing weaponry, which would be covered by federal law.) All the major airlines have a version of this document, and as Anthony Sabino, a lawyer from Mineola, NY, explained to USA Today, "There is no constitutional right to get on a plane."