Actually, you do have a right to fly on a private service once they've let you board. This wasn't the case yet in 2017, but the TICKETS Act clearly states:
> if the gate agent accepts a passenger for boarding after collecting or scanning the passenger’s boarding pass, the carrier is prohibited from removing the passenger from the flight thereafter.
> if the gate agent accepts a passenger for boarding after collecting or scanning the passenger’s boarding pass, the carrier is prohibited from removing the passenger from the flight thereafter.