A little bit horrifying to read, but I'm not entirely surprised. Years ago now I had a check-in agent give me someone else's boarding pass. Luckily the agent quickly realised their mistake and called me back to swap it (and ripped it up when I handed it back). I then noticed several other boarding passes scattered across the desk.
Luckily in OPs case they were attentive enough to have seen the gate scanner say 'ALREADY BOARDED' and knew something wasn't quite right and to bring it to the crew's attention. Assume in the scenario where this isn't reported to the crew and the 2 people just swap seats thinking it's not a big deal, a passenger count would eventually discover the mistake of an extra person onboard?