What do you mean by "officially"? I think you'll find that once a passenger's boarding pass is scanned at the gate, the system records that they've boarded. Certainly by the time the passenger is seated on the aircraft, they have boarded, whether you mean officially or unofficially or any other definition.
I mean just that--officially. When the flight is closed, the passenger manifest is final, the door is closed, and everyone is officially boarded. Scanning your ticket is not when you've boarded a flight. And even after the door is closed you may be bumped for many reasons, such as a mechanical issue leading to a plane change, weight and balance issue, safety issue, etc. Your personal belief of what boarded means would create passenger rights that don't exist, break other laws, and are impractical.