I believe if you change "catch" to "care about" you're closer to what the author intends, but you still have to add "non-runtime" in front of exceptions (The compiler doesn't force every method to throw or catch runtime exceptions thrown in child methods).
I circumvent that behavior by declaring (almost) all of my exceptions as runtime.
I don't think Java should require the addition of "throws" to the method declaration for non-runtime exceptions. It should just be implied.
Does anyone have an advantage that forcing the "throws" provides?