>... but somehow there's one in that scene.
...okay, I can see we're going to need to go step by step here. God damn, human beings really are bad at statistics.
1) Do you accept that there was at least one black gentleman in London in 1800? If your answer is anything other than "yes", you're an idiot.
2) Presuming you're not an idiot, is there a chance of encountering one on the Thames during an unusual snowfall? Not a certainty, just a chance, whether it's a 1 in 100 or 1 in 100,000,000. If your answer is anything other than "yes", then you're an idiot.
3) Having established that there IS a chance, what is the problem with showing a black gentleman? It simply means that a thing happened. It was unlikely, but not impossible.
Spoiler: UNLIKELY THING HAPPEN. In point of fact every day is filled with things that had only a million to one odds of happening, but nevertheless happened. The odds of being attacked and killed by a shark are 1 in 3,748,067. In 2015, six people died of shark attacks. The odds for them were the same as the odds for you, but it still happened despite there being less than a one in a million chance for each of them to get eaten by a shark.
>and not some honest attempt to accurately model the demographics of the period.
I can't see how you could possibly know that without sitting in the producer's room during filming, especially since it does accurately model what a crowd of 13 people could have looked like (except for the soldier's uniform, I guess. Mistakes happen).
>What are the odds?
More than zero, which is all they need to be to justify his presence.
>Can't do the math
This is hilarious because you're making the most fundamental mistake with statistics that anyone can make: the fact that something happens doesn't mean that it was likely to happen, and the fact that something didn't happen doesn't mean that it was unlikely to happen.