From a process point of view, and working backwards a bit from flatlander's scenario, there are 2 things going on here:

1) After a flight "Closes" at about 40 to 28 minutes before departure (often a bit earlier in out stations for some reason), there is a period of time when Standbys - mainly staff and Travel Trade, but sometimes passengers - are reconciled and seated where possoble. This is a fast moving process, similar to what visitors see in USA, where it is a more manual process done at the gate and typically involving a lot more passengers and seemingly vast amounts of typing. Now either the OP was a Standby, or the Flight Management Unit reopened the flight to allow a conventional booking through. Because both processes are going on at the same time it may appear that two people are in the same seat. This is one reason why FMU is loathed to open up a flight and can be somewhat snarky to agents who try to re-open a flight, but it can be done if HBO, it just makes life complicated.

2) In addition there is the usual shuffling of seats, usually involving at gate involuntary OpUps and many FTers at all sorts of levels have benefited from that. The system as an aircraft of 300 seats and it has (say) 290 passengers and one way or the other they can get everyone in. These passengers would have a confirmed seat at any point, but it may change. Furthermore it's perfectly possible to be sat in your seat, with a confirmed boarding pass, and it changes. Unless you have the App boarding pass (and the rather mighty assumption that it doesn't act up), then you would never know.

In both processes, going on at the same time, no-one would be placed in the same seat with another passenger. However unless their boarding pass magically refreshes itself it's always possible for someone to be holding an out of date boarding pass and not know it. Clearly the iPad would give the crew guidance here, though there's sometimes a short delay on that getting refreshed too, just to complicate matters.

A few months I had an overnight flight to Bombay, which had been changed from a 777-300 to a 787-9. I had therefore chosen in CW a "middle middle" seat 13E. I was settling in, pleased that Theoretical Seating had kept an empty seat next to me as boarding was coming to completion. Right at the end I saw a couple enter the aircraft and I recognised a WW crew member in mufti with her brother (as it turned out), walking slowly towards me, staring with that dazed expression at their boarding passes. As there was the empty seat next to me I had a feeling that I had been shifted, I quickly refreshed my App, and lo and behold it changed to 2K. Well as you can imagine I shifted myself very quickly. Funnily I wasn't challenged by the on duty cabin crew as I toddled up the aisle like a rat up a drainpipe, pausing only to shock the off duty cabin crew member by asking her how her dog was getting on (an old politician's trick that).