The word "correct" can convey the idea of "neat and straight", of conformance to some kind of norm or pattern. For example, a world is spelled correctly if it is spelled as given in dictionaries. A window shade must be cut to the correct width. In the 19th century a man's behavior might be called "very correct" if he said and did exactly the things required by the norms of the society in which he moved. Also in the language of the 19th century to say that a man "expressed correct opinions" meant that his opinions were uncontroversial and respectable in society. This statement was often meant to imply that he did not think for himself and that many of his opinions were wrong.
In contrast when we say that something is "wrong" we are invoking concepts of truth, justice, morality, and appropriateness. We are saying that these standards exist whether others acknowledge them or not.
As an example, more than a few 19th century gentlemen expressed the opinion that Africans and their own wives and daughters were not as evolved as European men and hence less intelligent. This idea was "correct" because it was expressed by influential thinkers such as Charles Darwin. But it was contrary to fact and hence wrong even then.
An example of this use of "correct" from the 20th century is the term "politically correct". Originally it was used as a criticism. Calling a statement "politically correct" meant that one felt pressured to agree with it whether one thought it was true or not.
Now let's return to your quote. It sounds like the medium's answer was "correct" because it conformed letter-for-letter to what was written on the letter in the man's pocket, but it was "wrong" because that address was the wrong answer to the question asked.
