Painted decks aside, decks were not allowed to simply weather. Holystoned, well-maintained decks became almost white or very light tan. Although I never served on any sailing ships in my Navy career, I did visit several ships with teak decks; I was always struck by how light they were in color.
We discussed this issue in a thread many years ago with a "La Flore" build, in which the builder presented the brownish, worn appearance mentioned above. We quickly ascertained that the British, Dutch, and American navies maintained their decks and these should appear almost white. The French and Spanish were not so inclined; their decks should have the worn, weathered brownish-gray appearance.
We should also note that the kit is depicted in her 1830's configuration with the Andrew Jackson figurehead intact. I doubt if she had gray painted decks then, but I couldn't swear to it. If the Constitution had painted gray decks, then I suppose the presentation is accurate. But, it does look strange to me; hence, its appeal.
Bill