Several interesting points in this thread. Some comments with my weight control officer chappie's hat on ... (and others already have made several of these)
Unfortunately, the request was so stupid, that I politely refused, told her I was comfortable where I was and asked her to explain her why.
Not necessarily stupid - it really depends on the aircraft, what sort of loading system the operator uses, LMC considerations, and where the initial loading position is in the envelope.
Probably better to not refuse the request (direction) as it would have had the commander's authority behind it, either implicit or explicit - certainly OK to query the reasoning in an appropriate way for whatever interest you may have had either at the time or, more usefully, later during the flight.
I don't believe a CC can calcuate the loading off the top of her head
Most unlikely that this was the case. Either the CC was applying prescribed loading rules or acting at the direction of the flightdeck folk. Mind you there is no reason why CC can't be highly expert in weight control matters - I've flown with some very switched on CC folk over the years.
its important to have the actual cofg as close to the calculated one for take off for setting the stab trim for the rotation
Not really - two options. Either rework the load to achieve the paperwork or, often a lot simpler if the final load is different, use the company prescribed protocol to record that different and refigure the numbers (usually by LMC protocols or redoing the sheet). Looking up a revised stab trim setting is not in the league of brain surgery and usually takes all of a couple of seconds.
once airborne you're free to move around the aircraft as we 'feel' trim changes and correct as required
That only goes so far. In some/many/most jurisdictions the operation is required to be constrained to keep the CG within the envelope throughout flight. It's not at all difficult to have folk wandering about the cabin and end up with the CG too far one way or another. Especially if the CG ambles too far aft, things can go from bad to worse fairly quickly.
our load sheets are designed in such a way that we split the cabin into sections or bays.
Typical approach but it should be noted that it reduces flexibility (and accuracy) while increasing ease of execution, management and general convenience.
the aircraft would fly if one or two passengers weren't in the required bay
A big difference between flying and flying while still being in the approved envelope. If the load sheet has had an appropriate error analysis it should have enough good guidance to provide for small misloadings. However, some don't and, if you move the load (even a passenger or two) while being near the limits, you could very easily find yourself outside the envelope requirements
loading of the aircraft MUST reflect the load sheet.
.. or you redo the load sheet for the revised load or do whatever other procedure is prescribed by the company to account for changed loading. Certainly should not be a necessary case of "having" to bust yourself to rearrange things to achieve an earlier load sheet iteration.
its much easier to ask a passenger to move than it is to move bags or cargo.
Exactly.
I suspect you were asked to be moved for a different reason and the cabin crew just used weight and balance as an excuse
It may well have been. Equally, it may have been so simple a case as that operator's loading system's being seat prescriptive - ie the CC noted that the passenger was not in the assigned seat and was only requesting that the assigned seat be used.