Sorry, but they were upgraded on one flight. If you change flights you have to play the game again. An upgrade is an upgrade. There was nothing wrong with the flight only that they got downgraded. No irregular ops, nothing, they just did not want to fly in coach. If it means that much buy the business class ticket. They basically whined enough and got supervisors to oversell a flight in coach and force an upgrade on a flight they were not booked on just to fly in business. That is not cool. If they had decided to change flights and had not been downgraded they would have to go into the queue just like everyone else. S**t happens, live with it. they got downgraded, they would have flown in the cabin they paid for. I also say very bad on UA for letting this person bully them into doing something they should not have done. Both parties were wrong.

And no, it did not belong to you but if they had not pulled the stunt it would have been yours and if that was the only upgrade seat you would have been in coach. And if you knew the reason why I suspect you would not have been happy, especially if you had a higher fare bucket than the OP.