This dream and its analysis has been greatly condensed but not changed in tone or substance from the entire chapter (!!!) it takes up in The Life of a Man. It feels entirely consistent with everything we know about Brinkley that he might have had a dream such as this one. Wood dabbled in dream analysis; he even wrote a book called Your Dreams and What They Mean. It’s also possible Wood could have completely invented this dream just so he could “analyze” it.
So this is landing somewhere between Seems Legit and Probable Invention. In any case, we’re repeating something we heard: it’s not verifiable, but we didn’t make it up ourselves.