Holy moly! There's an aspect to stroke rendering here that I've just never noticed before.
If you soften the Edge setting of a stroke when it's center-aligned, you'll see both inside and outside of the stroke soften or feather. But if you set the stroke alignment to outside or inside, only one side of the stroke will soften; the other side will be anti-aliased, almost as if that side is being rendered with the use of a mask. You can really see it if you remove the fill:
So what you're noticing in your example is the point or line along which two anti-aliased, semi-transparent edges are meeting: the fill and the stroke. And their point of overlap is not being intelligently coordinated in any way by Fireworks. So semi-transparent portions remain at their juncture, and the background shows through.
I think the simplest solution is to use a center-aligned stroke and adjust any object and stroke dimensions accordingly. You could also try selecting "Fill over Stroke" within the Stroke Options accessible from the bottom of the Stroke presets dropdown menu: This way, you can make a center-aligned stroke look more like an outside stroke, without the semi-transparent gap. Finally, I think that the Stroke effect available within Photoshop Live Effects (at the bottom of the Filter effects menu) somehow avoids the "gap" problem altogether, no matter what stroke alignment is used. So it's another option to explore.
Thank you very much for the detailed answer and help.
Tried Stroke effect within Photoshop Live Effects and it's perfectly do the job without "gap" between stroke and object .
Actually very surprised with such problem for such simple tool as stroke. I work with many Adobe vector and bitmap programs, including Photoshop but Fireworks is the first program that I have encountered such a problem.
p.s. Found an interesting article about some difference between native stroke tool and PS Live Effects in the FW CS6. Perhaps it will be interesting to someone else.