So, I just tried this, and it seems the answer is "it depends". AOL actually let me appear as "jerf.org", so it is not unreasonable that I thought this was the case. When I switched to using Yahoo, my OpenID got translated back to their idea of my id when I used it to log in. And I started flipping out, but decided to verify with another source before screaming too much. So I signed up for myOpenID and delegated to them, and once again I could appear as "jerf.org". I verified this using StackOverflow; with Yahoo I ended up on one account consistently, but with myOpenID and AOL I ended up on the "jerf.org" account regardless. I also verified StackOverflow was actually hitting my site on each request and not just caching my page.
So unless I screwed up, it is possible for it to work the way I describe, and it is possible for it to work the way you describe, depending. I'm calmed back down, but in general that's pretty worthless. I can not imagine why it should not always work the way I describe, it's the entire bloody point. Providers shouldn't even be able to screw me over that way.