In story terms, our characters see the symptoms and guess at the nature of his trouble, without knowing details; and always try to help him find a home in time and space. wherever he goes he tends to make ad hoc enemies; but also there is a mysterious enemy pursuing him implacably every when: someone from his own original time, probably. So, even if the secret is out by the 52nd episode, it is not the whole truth. Shall we say:

The Second Secret of Dr. Who: The authorities of his own (or some other future) time are not concerned merely with the theft of an obsolete machine; they are seriously concerned to prevent his monkeying with time, because his secret intention, when he finds his ideal past, is to destroy or nullify the future.