Good question.
There will be others with knowledge of the chemistry involved, i'm sure, but maybe leaving the fish whole and cold for quite a while allows the moisture in the flesh to re-absorb post mortem. Kind of like leaving a cooked steak to 'rest' after you take it off the heat - for the same period of time it was cooking? The juices are absorbed back into the meat, rather than running out if you slice it straight away...just my theory.
My recall of the rack you mention is that's how they keep the fillets in the fridge until cooking, not just before it's 'sealed'? Wonder if those folk put fillets directly on top of each other?
Like you, I iki my fish. I put mine in a chilly bin with 3 x 1l Charlies juice bottles filled with frozen salt water, and fresh salt water poured from the sea on the day.
By the time i get home, the water is pretty cold to put your hand in, and the fish are chilled stiff. In winter, the fish are almost starting to freeze! I used to buy salt ice and make a slurry, but now don't bother and have noticed no difference (EDIT: though reading Smudge's contribution below, maybe I need to re-think that!)
Most times, the first fish I've kept on a trip are say before 8am, and the last by maybe 11-12, and they don't often get filleted until 4pm or later - after everything else with the boat etc is cleaned and put away, and I've done some catching up with the boys and my wife, and the heat's gone out of the day.
My method is to put a paper towel on the bottom of a Sistema container when I start to fillet,and lay fillets with a gap between each piece on that layer, then another layer of paper towel, and so on, stacking them up as I go. I am now adept at pulling off another piece of paper from the roll with just my elbows and forearms to avoid mucky fingers on the roll! Final layer has paper on top, to absorb any condensation from the lid in the fridge.
No fillet touches another one.
With the method I never have any fluid pooling in the bottom of the container and the paper doesn't really get that damp.
Like yours, my fillets appear fairly 'dry', keep beautifully, and taste fantastic even after a few days.