Studies have not shown if fish liver oil helps with depression. Science sometimes fails to be like the thing that it studies; that is, slow-moving and focused. I have not the slightest idea if fish oil has any impact on depression (although it is probably as effective a placebo as anything else out there), but I'm pretty sure that you aren't going to get fast results out of a natural phenomenon.
Any scientific study must be funded, and most funding comes from the companies that profit from research - the ones making products that they can sell. Sunlight, plants you can pick from your own garden, and air just aren't going to be studied as serious treatments for anything since they're free and plentiful (unless a marketing person can find a way to sell us what we already have, a la pet rocks); things like fish oil and cow pies and cat hair are all common enough that it would be tough to charge a lot for treatments derived from them, also discouraging the really big research bucks. We aren't likely to see long-term studies on depression treatments that nobody can make money from.
There have been some amazing breakthroughs for treatments of all manner of diseases through new drugs. That doesn't mean that every drug is wonderful, nor does it mean that every disease's cure is in pill form. Well-trained pharmaceutical representatives earn a great living convincing doctors to prescribe their products, and no one is out there equally passionately pitching St. John's wort, taking a walk every day, fish oil, getting a puppy, copper bracelets, and believing in God (at least in doctor's offices). Plenty of alternative therapies may be effective, but the medical community isn't designed to find out.
Of course, I can't say that I would like the idea of being accosted by fish-oil salesmen.