What it should mean is that you should take both probabilities and costs into account when deciding what to do, as it's often worth doing something easy to reduce the risk of something unlikely but catastrophic.

But that doesn't mean you can just avoid thinking about it! "Often" doesn't mean "always". For example, it's worth checking the tire pressure in your car on a regular basis, because incorrect pressure could lead to a blowout at high speeds which can be most unpleasant, and checking it takes little time. But it's not worth checking the car for bombs every time you drive it, at least not for most of us, because the odds of being the victim of a car bomb for most of us are indistinguishable from zero.

A little thought reveals that this case is clearly in the second category, and thus calling the police is just a waste of public resources. But if you're incorrectly using "better safe than sorry" to mean "pick the option that appears to be safe without any analysis", you're not going to apply a little thought.