I know what you're describing. The <noscript> branch of piwik does the same thing, using a php file inside <img> tags, and I use it myself for some personalized tracking. To this day I get several requests a month for an image file that hasn't been used for tracking since late 2012. (It's some kind of archiver. Canadian, so I leave them alone.)
The main thing that's happening is: the page is trying to display the image, and can't find it, so it shows the "can't load the image" icon instead. The size of this icon is fixed, so even if the image is 1x1 pixel, the icon is 16x16 or whatever the browser says.
Now, when you're using an administrative gif (not the correct technical term, sorry) it's hardly ever necessary to have a collection of physical image files. Instead, each host's htaccess will have something like this--here cutting and pasting from my own version--
RewriteRule ^pictures/(hotlink|smallgifs/onedot) - [L]
RewriteRule ^smallgifs/dot\d+\.png /pictures/smallgifs/onedot.png [L]
RewriteRule ^smallgifs/dot[\w-]+\.gif /pictures/smallgifs/onedot.gif [L]
The first rule is your "the buck stops here" rule-- same thing you'd have with error documents. The second pair collapses all requests to a single physical file. (In my rule, the gif and png are separately rewritten because they tracked different information and therefore had different caching times. These follow the physical file, not the request.)
When it redirects
I'm a little worried about this. Who's redirecting and why? Trackers should happen invisibly in the background; a redirect is by definition visible.
The one thing you don't make clear in your first post is: Does the image on your own site physically exist?
If you're rewriting, look only at the target of the rewrite.
:: detour to test site to confirm something ::
Well, ###. I didn't see what I expected to see. In webkit-based browsers (Safari, Chrome, new Opera) and in MSIE 5, the bad-image icon shows up if there's a problem with the image file. (I tested both ways: using a bum filename, and explicit 403.) Don't know about newer MSIE. In Mozilla-based browsers (Firefox, Camino) and in Opera <=12 the alt text is used instead. This strikes me as a far better solution; does webkit reserve the alt for when the user has expressly chosen not to display images?
In your case the browser-specific behavior is useful because it alerts you to a problem. A different browser would display the alt text (for admistrative gifs, it should be "" the empty string) and you wouldn't see that there's an issue.