There actually is a connection. The link lies in population density rather than altitude, but its a link none the less. Take a look at any map highlighting the distribution of humans. We invariably congregate near coastlines where trade and commerce create jobs and revenue. Naturally, the higher the density of human inhabitants, the higher the crime rate.
Of course it could be that those of us living in the rarified air are simply too tired to get off our butts and knock off the local liquor store!
Revenge is a dish best served cold...
With a side plate of steaming entrails,
And a nice Bordeaux!