I have a solution to my immediate problem (details down below.) But the fix I found required hand-editing the svg file with all the unwanted fills. Once y'all see the corrections maybe you'll know how to get the same XML outcome through the Inkscape GUI. To achieve that, find the way I could not.
First off, though, let me respond to the folks who were kind enough to offer suggestions.
brynn:
I should also say that I don't know what autotrace is -- if it's a feature of Inkscape with which I'm not familiar, or if it's done with another program.Autotrace.exe is a separate application. It's a command line vectorizer available here:
http://sourceforge.net/projects/autotrace/. It's getting old and doesn't appear to be in active development any more, but I use it because a) it works just fine in its present state, and b) it's the only vectorizing app I can find that will do a centerline trace and doesn't cost hundreds of dollars.
For the record, here's absolutely everything I did to svg file written by autotrace, together with the Inkscape Fill and Stroke info I saw after each step:
1. open file in Inkscape
2. select Edit paths by nodes tool, click on any path/subpath in the image
3. press shift-ctrl-k (Break Apart)
After opening file:

After click with Edit-paths-by-nodes tool, before Break Apart:

After Break Apart:

The result of these three steps was as I showed in my first message, all the broken-apart paths filled with black.
while they are all selected, go to the bottom left area of the window, where it shows Fill and Stroke. If you right-click on Fill, then choose Remove Fill, you will have only the stroked paths leftover. Then you can see if the paths have been closed.Actually if I do this globally (all selected) there's nothing left over -- the whole drawing disappears and the edit-paths-by-node tool is no longer able to select anything.
Here's what happens if I remove the fill from just path3343:
1. Initial state, path selected:

2. Remove the fill from just path3343 (note the absence of anything connecting the little rectangles; I did not touch any stroke settings, just removed the fill.)

3. Now, the moment I click outside the bounding box, all those little rectangles (and the box) vanish, never to return. Or at least, no amount of clicky-clicky in this area with the edit-paths-by-node tool brings back either the box or the node rectangles.

All the other paths that are still filled, clicky with the node tool still displays their nodes and box fine.
Also I notice there is an awful huge amount of nodes. Depending on what all you plan to do, it might be helpful to use Path menu > Simplify. It will reduce the number of nodes.Oh, absolutely, that's one of the main things I want to do to. The vector graphic has so many nodes because the raster graphic I fed to autotrace was large (drawn in technical pen as big as I could fit on 8.5" x 11" paper and scanned at 300dpi; scanner output file is 2306 x 2484 px) and autotrace itself was set to preserve every last kink and wiggle of that I drew. Hence, as you said, lots of nodes. Certainly they're not all going to be needed but some of the paths are smoother and some are wigglier, and I want to see the effect that simplify has on each one before deciding yes or no. Therefore, Break Apart before Simplify. But that's where I ran into the wall yesterday, at the Break Apart stage.
prkos:
When I try to break apart a complex path made of lines they don't end up filled, I get exactly what you want.
Can you attach a SVG file or even one part of the file so we can see what's happening? There are what look like relevant pieces of the svg files below. And thanks for the nudge to look at the files directly, in a text editor. That's where I found my (non-Inkscape) work-around.
First off, here's the file as written by autotrace.
<?xml version="1.0" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 2306.0 2484.0">
<rect fill="#FFFFFF" width="2306.0" height="2484.0"/>
<path fill="none" stroke="#000000" d="M938 301C937.675 299.294 937.141 297.749 937.06 295.991C936.907 292.652 937.215...
...(some of the middle passages can be skipped

...
2444L599.199 2453L596.125 2456.98L593.736 2459.72L586 2465L577 2469.45L572 2470.6L559 2473.5L550 2477.71L543 2480.61L538.602 2483.19L537 2484"/>
</svg>
As brynn said, just one huge long path.
The first thing I did was write the file back out as an Inkscape .svg with no other changes, and also another Inkscape .svg after breaking the subpaths apart.
In the otherwise unchanged Inkscape-svg version, that also has only one huge path, the start of the path data looks similar to the autotrace version.
autotrace svg:<path fill="none" stroke="#000000" d="M938 301C937.675 299.294 937.141 297.749 937.06 295.991C936.907 292.652 937.215 289.294 936.523 286C936.089...
Inkscape svg:<path
fill="none"
stroke="#000000"
d="M938 301C937.675 299.294 937.141 297.749 937.06 295.991C936.907 292.652 937.215 289.294 936.523 286C936.089...
In contrast, after breaking up the paths in Inkscape and writing that file out, there are many path sections (expected) and they look different (not expected):
<path
style="stroke-width:3.09906881"
d="M 938,301 C 937.675,299.294 937.141,297.749 937.06,295.991 C 936.907,292.652 937.215,289.294 936.523,286 C 936.089,...
The references to
fill= and
stroke= are conspicuously missing. They aren't anywhere else in the file either, and some default is being applied that isn't what I wanted.
You'll see my hand fix right away, of course. It consisted of finding the start of each path section in the file that has the unwanted black fills, taking what looked like this
<path
style="stroke-width:3.09906881"
and supplying the missing lines to make it look like this
<path
fill="none"
stroke="#000000"
style="stroke-width:3.09906881"
260 paths for this file needed the fix. And this was just the leaf outlines. The next two scans waiting to be vectorized are much larger since they have all the internal shading lines (one has the thisaway-hatching and the other has the thataway-hatching). If this kind of hand edit turns out to be something I have to do often I'll certainly write a sed filter or something to do it by robot. Unless there's a valid global setting I could use in the XML. Or I can find the right way to do it in Inkscape.
druban:
The paths may just appear to be closed because they have a fill. Inkscape fills unclosed objects with a straight edge between first and last nodes; however, no actual segment exists there.Thanks for the correction. I did just assume they were closed because I've never used any other graphics package that could fill an unclosed path. Know better now, we does!
Thanks very much, brynn and prkos and druban, for your help and hints!
Jim