Apps and devices (mobile devices, web browsers, IoT, VR, voice assistants, etc.) routinely collect user data, and send them to first- and third-party servers through the network. Recently, there is a lot of interest in (1) auditing the actual data collection practices of those systems; and also in (2) checking the consistency of those practices against the statements made in the corresponding privacy policies. In this paper, we argue that the contextual integrity (CI) tuple can be the basic building block for defining and implementing such an auditing framework. We elaborate on the special case where the tuple is partially extracted from the network traffic generated by the end-device of interest, and partially from the corresponding privacy policies using natural language processing (NLP) techniques. Along the way, we discuss related bodies of work and representative examples that fit into that framework. More generally, we believe that CI can be the building block not only for auditing at the edge, but also for specifying privacy policies and system APIs. We also discuss limitations and directions for future work.