I don't understand what you mean by "they can throw me off"--that's only true in the same way that it is possible to do something unlawful, breach a contract, commit a crime, etc. You have rights as a passenger on an airline in which the U.S Government takes a rather active hand regulating. Those rights do not depend on owning the airframe or seat materials.
You have rights, yes, but the exact set of rights is different than most non-flight crew people think.
a very TL;DR summary is that they can throw you out, and you can sue them for it later if it was for invalid reason, but you still get thrown out. Similar rules happen on the sea, which results in hilarious summaries like "yes, a Disney Princess can sentence you to death and do the execution, if specific conditions are met" (condition being "evacuated on escape boat/device of a Disney cruise ship"). The summary is hilarious, but the same applies to plane's captain so long as flight operations are ongoing, including pre-flight preparation after embarking.
