What are the criteria for excluding subclass exceptions?

What I knew so far is that a subclass, if overriding a superclass method, should throw the same exception or subclass of the exception.

For instance:

It is right

class SuperClass {
    public int doIt(String str, Integer... data)throws ArrayIndexOutOfBoundsException{
 String signature = "(String, Integer[])";
 System.out.println(str + " " + signature);
 return 1;
 }
}

public final class SubClass extends SuperClass {
    public int doIt(String str, Integer... data) throws ArrayIndexOutOfBoundsException {
        String signature = "(String, Integer[])";
        System.out.println("Overridden: " + str + " " + signature);
        return 0;
    }

    public static void main(String... args) {
        SuperClass sb = new SubClass();
        try {
            sb.doIt("hello", 3);
        } catch (Exception e) {
        }
    }
}

This is not true

class SuperClass {
    public int doIt(String str, Integer... data)throws ArrayIndexOutOfBoundsException{
 String signature = "(String, Integer[])";
 System.out.println(str + " " + signature);
 return 1;
 }
}

public final class SubClass extends SuperClass {
    public int doIt(String str, Integer... data) throws Exception {
        String signature = "(String, Integer[])";
        System.out.println("Overridden: " + str + " " + signature);
        return 0;
    }

    public static void main(String... args) {
        SuperClass sb = new SubClass();
        try {
            sb.doIt("hello", 3);
        } catch (Exception e) {
        }
    }
}

But my question is: why is this code block considered the right compiler?

class SuperClass {
    public int doIt(String str, Integer... data)throws ArrayIndexOutOfBoundsException{
 String signature = "(String, Integer[])";
 System.out.println(str + " " + signature);
 return 1;
 }
}

public final class SubClass extends SuperClass {
    public int doIt(String str, Integer... data) throws RuntimeException {
        String signature = "(String, Integer[])";
        System.out.println("Overridden: " + str + " " + signature);
        return 0;
    }

    public static void main(String... args) {
        SuperClass sb = new SubClass();
        try {
            sb.doIt("hello", 3);
        } catch (Exception e) {
        }
    }
}