In my area some of the surprises you might find in the dark are: skunks,coyotes,cats.dogs,odd lawn ornaments and rocks,barb-wire fences,...
When the criminals fear what else may be lurking in the dark with them, how can crime not go down? Many of them probably couldn't see well at night to begin with.
Actually most homes are burglarized during the day when residents are gone to work.Home invasion typically target people known or thought to have cash,drugs,or guns;criminals want those three things. Best not to tell everyone how many pain pills any family member needs from the doctor,or flash cash, or brag about gun or art collections.
Most of my neighbors are of the 'fur and fang' verity too. I've been face-to-face with a bear on my back deck more than once.
Good advice about keeping quite about having pain killers and guns, etc. However, I doubt bragging about my "big Dob" is likely to draw in many burglars.
All of the break-ins in my area have been 'inside jobs' by people who knew the victims and what they had. Fights at meth labs are happening here in the 'back woods' too.
However, from the overall light pollution prospective, home security lighting is a much smaller problem (unless it's your neighbor's light shining on your scope) than street and parking lot lights, and lighting at large public and business buildings, like schools. That lighting is partly aimed at driving and walking safety, but also aimed at preventing vandalism, drug sales, gang activity, muggings, rapes, etc. I personally don't believe that all of our lighting efforts impact these types of crimes, while I think that driving and walking safety can be fully addressed with a combination of computer-controlled 'smart lighting', shielded lights, and even lower light levels. However, it will not happen while the public is convinced of the preventive value of the lights, and local officials are afraid of being sued for contributing to accidents, etc, because of their lighting. We need research, data, and public education to change that.