Java interface throws an exception but interface implementation does not throw an exception?

Question

I read this code where the interface throws an exception, but the class which implements it doesn't throw one or catch one, why is that? Is it legal or safe in java?

import java.rmi.*;
public interface MyRemote extends Remote {
    public String sayHello() throws RemoteException;
}

import java.rmi.*;
import java.rmi.server.*;
public class MyRemoteImpl extends UnicastRemoteObject implements MyRemote{
    public String sayHello() {
        return "Server says, 'Hey'";
    }
    public MyRemoteImpl() throws RemoteException {}
    public static void main (String[] args) {
        try {
             MyRemote service = new MyRemoteImpl();
             Naming.rebind("RemoteHello", service);
        } catch(Exception ex)
        {
            ex.printStackTrace();
        }
    }
}

Answer 1

A general rule of implementing and extending is you can make your new class or interface "less restrictive" but not "more restrictive". If you think of the requirement to handle an exception as a restriction, an implementation that doesn't declare the exception is less restrictive. Anybody who codes to the interface will not have trouble with your class.

— Stan James

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As part of the discussion at http://www.coderanch.com/t/399874/java/java/Methods-throwing-Exception-Interface