Atlanta has very high rates of violent crime across most categories, but it's in a very permissive state. On the other hand, Giuliani slashed crime rates in New York without doing anything to remove their draconian laws. There are simply too many variables in economics, policing, and demographics to boil things down to one factor.
Very good point, and if you're going to be intellectually honest, you have to be willing to "stink check" ALL of the arguments, even the ones that are favorable to YOUR cause.
As an example, I see lots of pro-gun folks who bring up Chicago's high murder rate and Draconian gun laws, and some of them are making the implicit (or sometimes explicit) argument that the gun laws are contributing to the high crime rate (fearless criminals, unarmed victims, etc).
But as Tom pointed out, there are cities with more-relaxed laws that have higher murder rates. It's possible that Chicago's gun laws are merely a failed attempt to reduce a crime rate that's high for completely unrelated reasons. Or perhaps the gun laws aren't a failed attempt at all - it's entirely possible that Chicago's murder rate would be even higher without those laws. Unfortunately, unless we have two cities that are identical *in every way* except for their gun laws, there's simply no way to prove causation.