The number of gun owners and the crime rate

Sen. Mike Lee (R-Utah) contends that "[I]n cities where more people own guns, the crime rate. . . goes down." http://huff.to/dJe67b

"If lenient gun laws actually reduce gun violence as the NRA claims, the U.S. should have the lowest rate of gun violence. However, a look at the numbers from other industrialized countries does not show this to be the case." International Gun Laws Show Firearm Availability is Related to Deaths http://bit.ly/i4ZVRd

Do you think that there is a (negative) correlation between the number of gun owners and the crime rate?
Do you think that there is a direct causal relationship between them?

If the percentage of gun owners--including guns for hunting--in rural areas is higher than in urban areas, and if the crime rate in rural areas is less than that in urban areas, then without any causal relationship between gun ownership and the crime rate, you can infer that there should be a negative correlation between the percentage of gun owners and the crime rate. But it does not necessarily mean that the guns reduce the crime rate. What do you think of this reasoning?