I can't recommend a single online distributor because I've never purchased through one. But, I recall a previous thread where one was recommended (I believe the retailer was out of San Diego or somewhere here in California). I think it was this place:
http://www.catalinaop.com/
You may want to consider talking to a local sushi bar or raw bar where they get "sashimi" grade fish. Although many wholesalers don't sell retail, some may. I go to two wholesalers here in LA that sell retail as well. They have all kinds of "sashimi" grade stuff. Also try an Asian market.
But, it's not true that most fish that are fresh can be served as "sashimi." You'll almost never see any freshwater fish (unless it comes from a wholly enclosed, circulated system) because freshwater fish can harbor bacteria, viruses and parasites that are harmful to humans. On top of that, most anadramous fish also are not or should not be served fresh or never frozen because they too can harbor bacteria, viruses and parasites that are harmful to humans. A prime example is salmon; salmon should generally be frozen before eaten uncooked. There are only a couple of brands of salmon that purportedly can be used without being frozen for raw preparations. And, Duckfat is right; the FDA recommends freezing (
http://www.fda.gov/downloads/Food/GuidanceRegulation/UCM252393.pdf).
Also, fresh does not equal safe or desirable for raw. I can't tell you how many super fresh, wild fish I saw (when I sold retail seafood for several years, including handling, cutting and selling lots of "sashimi" grade/quality fish) with numerous parasites in them, including California wild King salmon, various red tunas (soft spots), California Halibut, Black Cod, Rock Cods of various species, Sand Dabs, Pollack, etc.
Amazingly, you'll now see fish that were never previously used for raw preparations, which I imagine because many of the fishes traditionally used for sushi are just too expensive. That website above is now selling rock fish for sashimi. Black Cod is even being used which completely surprised me. That's one fish I would have never imagined being used for raw preparations. It's an extremely soft fish, with a gummy/mushy/slick mouthfeel when undercooked (I haven't eaten it raw and likely won't because of possible parasites - it's hard to tell in this fish because the color is dense; you can't necessarily see certain parasites).