Tom: If you read JK carefully you will realise that he just means that what you take to be you, the observer, is actually something that is observed. ie. the observer is actually the ego-mind or thinking-mind, and whilst you may take this to be the subject-observer, it is actually an object, ie. something that is observed.
Put differently, the thinking mind or thought often makes comments and commentary about the world, and so appears to be the observer-subject. However, if investigated, we can see that these comentarial thoughts are actually appearences or objects – ie. they are observed.