kksou -
I figured out some of the mysteries above. Google Reader will show a cache of articles previously contained in a feed. That's why it ALWAYS showed articles, even when the feed didn't actually contain anything.
I think my NewsFox plugin is broken - it doesn't work for any feed at the moment.
IE is providing a pretty reliable representation of my feed contents. I'm using it as my primary testing tool now.
As for your hack, like I said above, it works fine for every site I try it on but my production site. I was even able to modify my custom inserted code to test if the article is being displayed through a feed, and if so, skip serving images.
Now I have to figure out where the difference is between my production site and my staging site. Grrr.
The biggest issue I have right now is that I can't use Joomla 1.5 caching AT ALL if I want to have an RSS feed. For some reason when I turn on caching, the content of my feed goes away. The feed still works, it just doesn't contain anything. I've posted a question on the Joomla forum about it.
http://forum.joomla.org/viewtopic.php?f=431&t=292948
This behavior is easily reproducible on both my production site and my staging site.
So that's my update. For your part, your hack works and I was able to adapt my code to work with it well. Thank you again for your help.