"default" JDK is the one present in user PATH - let's say JDK6
if I want to use an alternative JDK5, I declare it on system configuration
But I still can't edit my project configuration to select JDK and it still run with JDK6
I need to declare a 2nd JDK so that the select box appears and I can configure my JDK5 build.

I suggest to deprecate support for "Default" JDK, as this is confusing and dependent on host system configuration.

To ensure backward compatibility, jenkins could detect at startup jobs that don't have a <JDK> element in config and automatically create a "System" JDK in global configuration based on System.getProperty('java.home').