So after the recent 6.0.2 update (again) failed to resolve this volume issue, I took the phone back to Apple.
My first visit -- brand new iPhone 5 with iOS 6.0:
I was basically told by the "genius" that there was nothing wrong with my phone and that I needed to do a restore (and not from backup). I was reluctant because I've had my iPhone backup going since the iPhone 3G, but finally I broke down and did it. Restored to a clean iOS 6.0 and the problem was still occurring, so I threw my backup back onto the phone.
... 6.0.1 comes and goes without fixing it ...
... 6.0.2 comes out earlier this week and I update...but it STILL doesn't fix the issue ...
My second visit -- same iPhone 5 with iOS 6.0.2:
I told the "genius" that I had been in before with 6.0, tried the restore and it didn't work, so I waited through 2 OS updates that both didn't fix the issue. I was reproducing the issue to him in a loud Apple store, so he said not to worry about it and that he'd swap out phones for me to (now) rule out a hardware issue. I'm a software developer, and everything about this issue screams software, but there's always a chance. So I leave the Apple store with a new iPhone 5, and did a "restore from iCloud backup" first-thing. Since yesterday I've been using the phone as I used my original one and I HAVE NOT encountered the weird volume issue yet. This includes using Siri, plugging in headphones and plugging in my car's AUX (headphone jack) cable, and turning my ringer volume up/down and silent on/off.
SparkNotes:
1. iPhone 5 with iOS 6.0 had volume issues.
2. Got rejected at Apple genius bar.
3. Restore didn't work.
4. 6.0.1 and 6.0.2 didn't fix it.
5. Second visit to Apple store, left with new iPhone 5.
6. Restore from iCloud backup.
7. No issues for 18 hours so far.