Roger hinted but didn't quite state that ResultSEts and some other things in
JDBC are database resources, not
Java resources. Java is pretty good at memory management, although it is still possible to create memory (or 'resource') leakage it isn't quite as easy as it once was.
Things change when you mix Java with external applications. If these applications manage a finite number of resources, Java can try to get it right for you but may not be perfect. I believe you can have similar problems in AWT if you don't close some of the resources.
Personally I prefer the defensive technique: Always try to make sure you release resources when required, because if it ever becomes an issue it will take you two weeks or more to diagnose and fix the problem