Should I use a narrower saddle on a road bike than I would on my hybrid commuter?
Yes, a more aggressive stance requires a narrower saddle.

Your pelvic bone is a fairly complicated structure, but there's basically a triangle that you sit on with a saddle.  There's two bumps ("ischial protrusions") at the back end that take your weight if you're sitting with your back straight up (such as on a chair or the saddle of a cruiser or dutch bike). The front point of the triangle is the "pubic symphisis" which you don't sit on. Between there it's basically slightly curved like the bottom of a rocking chair.

Look here: http://en.wikipedia.org/wiki/File:Gray237.png
Here: http://en.wikipedia.org/wiki/File:Gray235.png
And here: http://en.wikipedia.org/wiki/File:Skeletpelvis-pubis.jpg

As you rotate your hips forward (for a more "aggressive" position), your hips should be rotating forward and your back staying relatively straight. Because of that, the part of that ischial/pubis structure that you sit on is more towards the narrow front part and the saddle should be narrower. This can also affect the desired tilt of the saddle.

Also, in general, if you're riding more aggressively, all that pedaling removes some of the weight from the saddle and makes any kind of rubbing against the saddle more of a problem, which are additional reasons aggressive road riders may want a narrower saddle.