OK… Several years later in January 2014 I had this same problem only in Windows 7 (i.e. not in Windows XP). To get some background see my first two posts on this topic here and here. These two posts are back from 2008. So I asked this question on StackOverflow (SO).
Luckily I got some very useful comments and answers there. They helped me to finally resolve this mystery (about the JVM executables which keep on reappearing in C:\Windows\System32).
As some folks noted in their comments to my SO question… it’s strange for any 3rd party programs/apps to install executables in C:\Windows\System32. That looks completely illogical… And that is what started the whole confusion some 11 years ago 🙂
Anyway… it’s good that the problem was finally solved. The solution is in the accepted answer here.