According to this site (
https://en.wikipedia.org/wiki/List_of_countries_by_intentional_homicide_rate), the European UK rate listed was 1.0 per 100,000, the Cayman Islands rate was 14.7 per 100,000, and the US rate was 4.7 per 100,000. The Texas rate from here (
Page not found | Death Penalty Information Center) was 4.3 per 100,000. So I don't think you can make any solid inference whatsoever about whether gun control in the UK or the Cayman Islands leads to a lower murder rate or not. The Cayman Islands rate is 3 times the US rate and 14 times the European UK rate. Demographics, socioeconomics, and other concerns have a much higher impact than availability of a specific weapon type.
I think the point that was trying to be made wasn't that the Cayman Islands should ignore their laws in deference to foreigners. I think the point was that a single bullet of ammunition is not a threat in the absence of something to fire it with, and in absence of evidence that the carrier was attempting to smuggle it in for nefarious purposes, it is logical to assume it is a mistake. The government officials in those cases might want to consider a punishment that will make them remember to check their bag better next time (or not be a bone head and travel using your range bag). Instances where people show up at the airport with a gun in their bag are much more serious, as are cases where somebody arrives with a box or two of rounds...which might indicate potential for smuggling to a black market. One round in the bag of somebody leaving the island is evidence they are an idiot who made a mistake and should be punished...but it should be punished for what it is, stupidity, not evil intent.