If only it were that simple, but sorry no, you can have a 1.0 correlation between two variables and they can still not be causally related. They tried the actual experiment in the UK, and just found that once guns were outlawed, assault with other weapons like knifes went up (
https://www.bbc.com/news/uk-53443246). So yeah, GUN crime probably went down, but crime as a whole didn't. What I would guess is that countries with enough resources to enforce strict gun regulation, such as Japan, probably have stable, civilized societies where crime-culture isn't necessary - that can't be said for many parts of the US, although the US isn't particularly high in crimes like homicide (we're ranked 94th despite being the third largest country).
Besides, the correlation between gun laws and crime levels probably aren't as high as Alan would have you believe. The country with the highest crime rate, Venezuela, outlawed guns almost a decade ago.