Statistics about traffic flow and people's movement gathered from multiple geographical locations in a distributed manner are the driving force powering many applications, such as traffic prediction, demand prediction, and restaurant occupancy reports. However, these statistics are often based on sensitive location data of people, and hence privacy has to be preserved while releasing them. The standard way to do this is via differential privacy, which guarantees a form of rigorous, worst-case, person-level privacy. In this work, motivated by several counter-intuitive features of differential privacy in distributed location applications, we propose an alternative privacy loss against location reconstruction attacks by an informed adversary. Our experiments on real and synthetic data demonstrate that our privacy loss better reflects our intuitions on individual privacy violation in the distributed spatio-temporal setting.