Java 7 - Precise rethrow with a final Exception

In previous versions of java, rethrowing an exception was treated as throwing the type of the catch parameter.

For example:

public static void test() throws Exception{
    DateFormat df = new SimpleDateFormat("yyyyMMdd");
    try {
        df.parse("x20110731");
        new FileReader("file.txt").read();
    } catch (Exception e) {
        System.out.println("Caught exception: " + e.getMessage());
        throw e;
    }
}

In Java 7, you can be more precise about the exception being thrown, if you declare the exception final:

//(doesn't compile in Java<7)
public static void test2() throws ParseException, IOException{
    DateFormat df = new SimpleDateFormat("yyyyMMdd");
    try {
        df.parse("x20110731");
        new FileReader("file.txt").read();
    } catch (final Exception e) {
        System.out.println("Caught exception: " + e.getMessage());
        throw e;
    }
}

My question: The docs say that I need to declare the Exception final. But if I don't, the code above still compiles and works. Am I missing something?

References:

Project Coin: multi-catch and final rethrow
Add more flexible checking for rethrown exceptions