In reproducing a conversation, one throws it, of course, into conversational form; the words used may not have been exactly those which were employed—but still they give the effect of what passed.
Sir Robert Finlay
Attorney for the White Star Line
British inquiry into the loss of the Titanic
June 27, 1912
Finlay was right in the context of the inquiry: the surviving officers of the ship might not recall all of the exact words that were spoken on the bridge, but they could testify as to whether, for example, they discussed the weather with the captain.
If I were citing such a conversation, I would use an indirect quote: I might write, for example, The captain told the officers that they should call him if they saw the least bit of haze—no quotation marks, just a summary of what was said.
What if you do know the exact words that were said? “Some journalists say it’s fine to ‘improve’ quotations as long as the meaning isn’t changed,” wrote Fawn Germer in “Are Quotes Sacred?” (American Journalism Review, September 1995). “Others argue that the practice is dishonest.”
“If only sources could say it right the first time,” wrote Germer. That implies another choice: ask the source, “Did you mean to say …?” This gives the speaker a chance to provide a better quotation; this may be a good choice for writers on a relaxed schedule, but in the new business there may not be time.
Germer covered the subject thoroughly, noting, “While some believe editing quotes is doing the source—and the reader—a favor, others say there’s simply no excuse for it.” The article is well worth reading.
I follow the Associated Press rule: Never alter a quote.