You're probably right about the reading all of the Apache docs and HTTP specs, Jim. Honestly, though, with you and g1smd passing out the free advice, the learning is proceeding quite quickly. ;)
FYI, the way I figured out the /style.css and /script.js issue was through the use of LiveHeaders, which have been an occasionally-useful tool for quite some time ... up to a point.
The "light bulb" in the latest (and last) issue in this exercise came on when I read 'you have added a subdirectory called "/article" to all of your URLs', which helped me to recognize that the rewriting is more than simply finding the location of the resource.
It was not a matter of not having the information, it was an *interpretation* of the information that was hanging me up, conceptually. No amount of book larnin' can help with that. ;) Sometimes discussing the data you have been studying to exhaustion is the best idea. You provided the interpretation that made sense of the data.
The rewritten path BECOMES the web path, for the browser. The name, location and other identifying features of the resource being displayed is irrelevant to the browser ... it eats what the server feeds it.
The server fed it "/article/blah-blah", not "/index.php?p=123", therefore a request for "style.css" would be relative to the "/article" directory the browser "thought" it was in.
(Please forgive the anthropomorphisms. It's a mechanism I sometimes use to simplify behaviors to understand them better ... to give them a familiar context. I want to assure you that I don't *really* believe that a web browser "thinks" anything, nor that there are any actual "mysteries" involved with computer programming.)
So .. THIS "mystery" is solved, and everything is now consistent. I may still take a few weeks to study the HTTP specs, as it's been a long, long while since I did so ... like somewhere around 20 years. Believe me, though, when I tell you that with this issue the Apache docs have been pored over again, again, and yet again ... and look where I came out! :) Not too far from the truth. Just needed some Apache doc translation, which y'all have been kind enough to pass along.
Thanks again, guys. As far as I'm concerned, I'm done.