Diana is so crazy for the moon

Yea true

Full moons disrupt established circadian rhythms by confusing light dark cycles, which can create effects similar to jet lag (foggy head, drowsiness). The effects would be more prevalent in those people that are already less mentally stable. It isn't only humans susceptible to this, Cats, dogs and many other animals also experience similar effects.

EDIT: Humans, and animals in general, are more prone to rash decisions when their circadian rhythms are disrupted. Many large companies have policies in place to prevent businessman / businesswomen from making deals / signing contracts within 24 - 48 hours of traveling across a certain number of time zones because of this. On a more primitive note, the full moon was both the best chance for nighttime hunting, as well as the best night to be hunted at nighttime. It is programmed into humans and many other animals to be on higher alert for prey /predators come a full moon.

Back to your post, no, that is not how subjectivity works. The fact that there is an increase in violent crime on a full moon is a purely objective data point. Your comment is a point of subjectivity, as well as density and naivety. Sure 1/1000 violent crimes might be explained by asinine motives like this, but those people are not likely to be truly crazy, rather just jerks pushing semantics too far.

There truly is a correlation, but in highly developed / safe areas, where people live every day with a higher sense of security, the impact is naturally less.

I have seen many people who I would not consider superstitious to swear by it so I tend to believe it. Obviously it's not a supernatural effect, if lunacy is a thing it is probably due to some encoded behavior deep in the human genome, perhaps more visibility at night creating a psychological trigger to be wary of predators thus putting people more on edge leading to more cases of violence.