In this paper, we consider remote reconstruction over wireless networks when simultaneous accuracy at the legitimate receiver and confidentiality against eavesdropping are required. These two objectives are often treated separately, even though they arise from the same update process and are marginals of a joint reconstruction event. This paper introduces confidential reconstruction accuracy (CRA), a metric to capture the joint event in which the legitimate receiver reconstructs correctly while the eavesdropper fails. Under randomized stationary policies, we develop a three-dimensional stationary analysis and derive closed-form expressions for the long-term average CRA and the optimal transmission probability. The results show that conventional marginal analysis can misidentify the optimal policy and misestimate the achievable simultaneous accuracy-confidentiality performance. They also reveal nontrivial behaviors: more frequent transmissions or better legitimate channels do not necessarily improve joint accurate and confidential reconstruction, and when the eavesdropping channel is strong, improving the legitimate channel alone may be insufficient. Finally, the framework induces the spatial safety boundary in a geofencing setting for secure remote reconstruction.

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