Ah, but evryone else only gets those kind of yields when they tie themselves down to a highly rigid civic/improvement pattern. Sure, you CAN do somewhat better if you do Agriculture/Aristocracy and only build farms, but then you're screwed for Hammers. Lanun, on the other hand, have all the food they need from the water, can build mines and workshops for hammers without worrying, can cottage pretty much everything else, AND can benefit from superior civic choices.
The thing is, although the Lanun do get maritime bonuses, they aren't ONLY on the sea... they can still do everything on land that everyone else can, except farm. Since they don't need farms, they build other, more useful things. After all, it's been a common axiom throughout civ that unless you're GP farming, you build as few farms as possible. Tweaks like Agriculture and Aristocracy don't change that. After all, every farm built is a town foregone. IF you're getting your food somewhere else anyways... why not cottage everything? The Lanun AI usually does this... and it's a perfectly good strategy.
Also, so far as synergy goes, do note that Hannah is Financial, and thus gets an extra commerce from all water squares, too.