Phil,
It really is all about the paperwork. As you have said, moving one person a few rows is not really going to make a lot of difference to the actual operation of the aircraft in the case where there's one hundred or four hundred passengers or so.
However, the original poster did not mention which airline he was traveling on so I have no idea of the load planning system used in that case.
Weight and balance systems are required to be certified by the authorities, this can make it very expensive to set up computerized systems for smaller carriers. In a previous post of mine in this thread I listed nine airlines with which I have personal experience as a load planner.
Every one of them had a different system.
Two of them used Microsoft Excel spreadsheets, those being ProAir and Kittyhawk. In the case of ProAir they did not have assigned seating, the aircraft cabin was divided into zones. After the doors were closed the flight attendants would carry out a head count for each zone, pass this to the cockpit crew and they would give me those numbers by radio. I would then plug in those numbers into the spreadsheet along with the numbers of bags loaded fore and aft, also called in by radio to me by the ramp staff. When all was plugged in the spreadsheet would give me a bunch of numbers such as ramp weight, take off weight and most importantly the stabilizer trim setting. There were six numbers in all if I remember correctly but I don't remember them all.
I would then call these numbers to the cockpit crew and if all was hunky dory they would do what they need to do with them and be on their merry way.
BUT
Sometimes the passenger load would be bad or the bag counts would be bad and it would lead to the aircraft being out of trim, in these cases the spreadsheet would not give any numbers, just blank boxes. I would have to fix it by adjusting the passenger zone numbers until the spreadsheet was happy and presented me with final numbers. Passengers were moved because it would take too long to move bags. Once I adjusted the load and had numbers I would call the crew and tell them to move X numbers of passengers from zone B to zone C or something like that, then I could give the crew their numbers. Obviously the further you can move the passengers the fewer passengers you have to move.
Now here's the thing......They could not leave without my numbers. Did they always ask the cabin crew to move that one passenger from zone b to zone c? I have no idea. From my point of view my neck was clear of the noose because I had a good load sheet and the numbers I gave them were on the cockpit voice recorder. I'm sure some captains probably asked the cc to move that person, some probably did not. That was up to them.
So.....what we have here in the original post is a situation where numbers needed to be corrected to get an in trim aircraft on paper for the files and obviously a captain who wanted the change to actually be made, that's his perogative. What we also have is a person who claims to be a pilot and yet when told he needs to move for w&b purposes gets all uppity about it. Maybe he made it known that he was a pilot and the CC thought he would be the most co-operative person to move because of that. Maybe he was actually deadheading free of charge, if that was the case I'd throw him off if I was the captain.
Anyway I could go on about other systems but I think that's enough to answer the questions.
Oh and as to whether the aircraft would fly ok without the adjustment, I know of an airline that was fined big time when it had a B737 takeoff with a load sheet that was so wrong the take off center of gravity was not only outside the envelope it was outside the margins of the graph and almost off the page!!!! The agent doing the load sheet had reversed many of the numbers when extracting them from the books.
I ran the numbers for that flight myself and was amazed that the aircraft completed the flight without crashing, but it did.
So there you have it.
Hope that helps.