When Uncharted: Drake's Fortune released all the way back in 2007, regenerating health was the latest game design trope that was being bandied around. Every one of Nathan Drake's adventures has used this health system, but this little tidbit from Naughty Dog animator Jonathan Cooper suggests that it wasn't really a health system at all.
That's right: the desaturated screen and red outline actually signified Drake's luck running low, rather than his health. Amy Hennig, the original creator of the series, took to Twitter to confirm this: "True! That was the original intention (to stay more aligned with the spirit and tone of the films we were homaging)." It does make some thematic sense, sure, but it also explains why his "health" is able to regenerate. Not only does this fit the tone of the games, but it also gets around the idea that a person can simply hide and wait for their bullet wounds to heal. Clever stuff.