Reachability is thought of as the most basic service provided by today’s Internet. Unfortunately, this does not imply that the community has a deep understanding of it. Researchers and operators rely on two views of reachability: control/routing- and data-plane measurements, but both types of measurements suffer from biases and limitations. In this paper, we illustrate some of these biases, and show how to design controlled experiments which allow us to "see" through the limitations of previous measurement techniques. For example, we discover the extent of default routing and its impact on reachability. This explains some of the previous unexpected results from studies that compared control- and data-plane measurements. However, not all limitations of visibility given by routing and probing tools can be compensated for by methodological improvements. We will show in this paper, that some of the limitations can be carefully addressed when designing an experiment, e.g. not s...