I am adding this additional page on the topic as the interest in this remains high and I've recalled more on the subject over time.
It must be said that the additional anecdotes cannot be vouched for as definitely as my personal experience in the case of Bernstein. A case in point is Tchaikovsky where additional contradictory evidence apparently exists, But I'm reasonably certain that Tchaikovsky did indeed have it.
An even less certain case is that of Gustav Mahler. He seems to have had absolute pitch as a child but gradually lost it as an adult. The story I read somewhere is that Mahler was rehearsing an orchestral work and stopped the orchestra saying that something was wrong. Up popped Bruno Walter who was listening to the rehearsal and he proceeded to tell Mahler exactly what was wrong. (It was in one of the trumpets I think.)
Walter, by all accounts, definitely had absolute pitch so the story rings true.
Sir Georg Solti, on a DVD "Solti: Orchestra! (1991)" told Dudley Moore that he had absolute pitch (Dudley said he himself did not have it.). Though I don't doubt Sir Georg's word, there is a story about an unnamed conductor who boasted of his absolute pitch until his musicians decided to put this to the test by secretly rehearsing a few pages which they played for him, at first, in a different key. The maestro was none the wiser till the orchestra inevitably fell apart.