I can totally see the appeal of flying in an almost empty 747, but at least according to this source[1] that makes a truly shocking 1MPG between the five of you. I can't help thinking the world would be a bit better off if they'd just apologised, and put you on the next flight.
[1] http://science.howstuffworks.com/transport/flight/modern/que...
Sometimes the sizes of the passenger streams between two destinations aren't perfectly in balance. This is most clearly visible on shuttle services between a small and a large city - busy going to the large city in the morning and to the small city in the evening, and semi empty in the opposite directions.
Also seasonal flights - the first flight of the season to depart the destination (and the last to arrive) will often be pretty lightly loaded.
When that situation arises, you will need to reposition a less-than-full aircraft, otherwise your operations obviously falls apart. The GP clearly experienced an extreme case of this, but most likely that aircraft was being filled up at its next departure, and so needed to be there.
This is obviously expensive for airlines, so they try all they can to fill up these flights - which explains that the cheapest tickets are often on times that will be slightly odd or inconvenient, at least to business travellers.
Also, schedules are built around keeping the plane in the air as much of the time as possible, which sometimes means there's a mostly-empty "positioning" flight to get a plane to where it needs to be to carry a full load. I know with US Airways, for example, you can sometimes randomly snag a seat on a widebody international plane between Philadelphia and Charlotte (usually coming out of maintenance and onto transatlantic service, or switching which hub the plane operates from), and on Delta you can occasionally fly a 747 domestically between Atlanta and Detroit (to get the 747 in position to fly from Detroit to destinations in Asia).
I wanted to try first class on the 777 when it first came out, so I just connected in DFW for a PHX-ORD trip, and did the DFW-ORD segment on a 777.
As it turns out, domestic flights are GREAT in big aircraft. (Though I do like the smaller A321Ts too. International-class accommodations, but a really small feeling, like a private plane.)