You can't have an interface implementation throw exceptions not declared in the interface, hence all implementations of a given interface have to declare the same failure modes. And then everything is nicely coupled.
https://docs.oracle.com/javase/7/docs/api/java/io/ByteArrayO...
If an implementation of an interface can throw an exception that its interface doesn't declare, that breaks the abstraction. How can you safely use the interface? You either have to catch Exception (which is effectively the same as wrapping every exception in some InterfaceException class), or give up on handling any Exceptions thrown by the interface.
That's just how I phrased it 18 hours ago. The thing I find bad about it is not that exceptions have to be declared in the interface, that's good, it's that every implementations will have to declare them also, even in the case that a particular implementation has no failure mode.
But in general, of course an implementation can't just randomly add checked exceptions, because that would violate the Liskov substitution principle.