How do I completely uninstall ALL remnants of ARD so I can cleanly reinstall it?

Somehow I had ended up with mismatched client and admin versions on one system. At least, I think I did... I believe I had read strange errors stating such a while ago.

So when ARD on this specific machine started forcing re-authentication, always said "Access Denied" in the Computer Browser (while still allowing Control sessions), and extremely slow performance, I decided to reinstall ARD.

Installing over top of the existing installation didn't solve anything.

I then followed steps outlined in Uninstall or disable Apple Remote Desktop - Apple Support. I didn't encounter any problems during the process.

But then I took a look at the Computer Browser in ARD on another computer... and it shows that the fresh, cleanly uninstalled Mac (which shouldn't be showing up at all at this point) was sitting there with ARD installed, listening for connections, and authenticated (ready for a Control session). I restarted both machines, started ARD on the "admin" computer and lo and behold... there is the ARD-less (supposedly) machine, sitting there in the browser, little blue dot indicating all is well and ready for ARD sessions.

How is this possible when I actually dropped ARD into the trash? Basic Screen Sharing is also turned off on the supposedly in-accessible-by-Apple-Remote-Desktop.

ARD 3.7.1 running on OS X Server Lion 10.7.5.

^--------- This is what the browser on another Mac claims. On the 10.7.5 Server I can't check because it's supposedly uninstalled.