We study a secure integrated sensing and communication (ISAC) model motivated by the need to simultaneously exploit the sensitive attributes of wireless devices, such as their location, and communicate securely. Specifically, we consider a state-dependent binary-input two-user additive white Gaussian noise (AWGN) broadcast channel, in which the channel state sequence consists of two components, each affecting a receiver, modeled as independent and identically distributed (i.i.d.) correlated phase shifts to approximate the location-dependent signatures of the receivers. The objective of the transmitter is to simultaneously estimate the channel states while reliably transmitting a secret message to one of the receivers, treating the other as a passive attacker. We characterize the exact secrecy-distortion region when 1) the channel output feedback is perfect, i.e., noiseless with a unit time delay; and 2) the channel is degraded. The characterized rate region offers an outer bound for more complex secure ISAC settings with noisy generalized output feedback and non-degraded channels. We also characterize the secrecy-distortion region for reversely-degraded channels. The results illustrate the benefits of jointly sensing the channel state and securely communicating messages as compared to separation-based methods.