Well, Apple is pretty much in charge of updating the software on your computer, if it's software that comes with the OS (like Java). Of course, you can always install your own version of Java, but for a new computer user, that would be a very daunting task.
If you upgrade your OS X software to either 10.2 or 10.3, your Java sites should work as expected. Which site is it? I can check, since I'm on 10.3, and verify that if you did indeed upgrade, that it would work. Let me know!