Originally Posted by chornedsnorkack
I was actually more interested in what happens when a passenger on flexible ticket attempts to switch to a different flight on the same carrier.
I think you are inventing complications here. If a flight is full up to its booking limit then you will not be able to get a seat on it, whether you are trying to pay for it using cash, credit card or exchanging a flexible ticket on another flight.
The issuing airline is the airline on whose paper the ticket was written, and who is holding your money. They will usually but not always be the first airline in a multi-sector journey involving carrier changes although strictly speaking they don't need to be part of the itinerary at all.