You really should read the analyses people are posting about that. I don't know of any credible people saying it's flat-out always illegal to remove someone after allowing them onboard, but I do know of credible people saying the legally and contractually permitted reasons for it are few in number and the reason given in this situation (to make room for deadheading crew) is not one of those permitted reasons.

That's not a "tenuous interpretation of the law". That is the right interpretation of the law. Once you have been accepted as a passenger and boarded the plan and been seated, there's no legal reason for the airline to eject you without cause.