A completely gratuitous post today, as my hotel does not have BBC America.
Yesterday's Google Doodle was about Albert Szent-Györgyi, who I had never heard of. Wikipedia informs me he discovered Vitamin C, and "was also active in the Hungarian Resistance during World War II and entered Hungarian politics after the war." Which is very cool. But still, I'd never heard of him. Likewise, I'd never heard of Henry Avery (or Every) until The Curse Of The Black Spot. Where it didn't matter, because it was a story about PIRATES! (And interdimensional holo-nurses.) Liberties were there to be taken. But ultimately you don't want to offend people unduly.
So how do you treat real people who aren't that famous? Give the portrayal a bit more leeway, or treat them as important figures that the audience (the players) are just learning about?
Or how about treating a "Who's Who" level character in an unexpected way? In The Impossible Astronaut and Day Of The Moon, Nixon sided with the heroes to help a frightened child.
When I ran a one-shot set during the Cortez campaign, I kept the man himself off camera as I didn't know who at the table would know the history or might have a strong opinion about it.