Yes, this is expected behavior. It's because the paint bucket type of feature is meant for raster graphics, but because of general demand for it, has been added to Inkscape (which of course is a vector graphics app). In order to help address the issue of the thin strip of uncolored area around the border, there's a setting in the Paint Bucket

control toolbar called "Grow/Shrink by". So you can set it so that it fills a slightly larger or slightly smaller area than is defined by the objects or paths that enclose the area. I think the Threshold setting can also affect the same issue, but I'm not positive about that. Neither is a perfect solution. But paint bucket probably never will work perfectly in Inkscape because of the raster vs vector thing.
However, there IS a benefit I've found to using the paint bucket in the vector arena. What happens is that not only does this tool add color to an enclosed area, it creates a new closed path that is filled with whatever color you've chosen. So I've found that after I zoom in a little, I can use Snap, and move the nodes of the new path to lie directly on top of the paths and/or strokes that define the enclosed area. In certain situations, I do have to mess with the node handles, to avoid gaps and overlaps. And it does take more time to do this. But this technique results in the appearance of a Fill, with no uncolored strip between (in this situation where a real fill can't be applied).
[Edit] A couple of tips that work for me -- I use Grow by 0.50. Also I've found that if I zoom until the area I want to fill w/paint bucket just fits my screen, less of an uncolored area results. You can use the Zoom tool and drag-select the area, to do this.