That exact phrase is repeated numerous times on what appears to be thousands of web sites. However, in the 50 that I took a look at, none of them sourced it. The best I have found is reference to a law passed on March 9th, 1562. Apparently an anti-obscenity law. As to how strictly it was enforced, I again am only getting references to the law itself (without any actual text of the law).
Given this pattern, I would suspect that perhaps an anti-obscenity law was passed on that date in Naples, but it was not strictly aimed at kissing, but other behaviour deemed immoral by the local magistrates/clergy/rulers. Kissing was just one thing mentioned.
I will continue to search for the original text of this law, but History is not my greatest subject, so I am leaving this as a wiki for the community.