Static scene videos, such as surveillance feeds and videotelephony streams, constitute a dominant share of storage consumption and network traffic. However, both traditional standardized codecs and neural video compression (NVC) methods struggle to encode these videos efficiently due to inadequate usage of temporal redundancy and severe distribution gaps between training and test data, respectively. While recent generative compression methods improve perceptual quality, they introduce hallucinated details that are unacceptable in authenticity-critical applications. To overcome these limitations, we propose a positive-incentive camera (PIC) framework for static scene videos, where short-term temporal changes are reinterpreted as positive-incentive noise to facilitate NVC model finetuning. By disentangling transient variations from the persistent background, structured prior information is internalized in the compression model. During inference, the invariant component requires minimal signaling, thus reducing data transmission while maintaining pixel-level fidelity. Experiment results show that PIC achieves visually lossless reconstruction for static scenes at an extremely low compression rate of 0.009%, while the DCVC-FM baseline requires 20.5% higher Bjøntegaard delta (BD) rate. Our method provides an effective solution to trade computation for bandwidth, enabling robust video transmission under adverse network conditions and economic long-term retention of surveillance footage.