Streaming video understanding demands direct responses from the causally observed prefix of an unfolding video. Existing systems add inference-time memory, retrieval, and compression, yet a training-free sliding-window baseline already matches them. We therefore fix a memory-free recent-window protocol and ask how far post-training alone can go. Reinforcement learning with verifiable rewards fits this regime poorly, encouraging long ``think-then-answer'' generations, while on-policy distillation (OPD) supplies dense token-level teacher supervision on student trajectories but is stable only when both models train in thinking mode. These observations lead to \textsc{StreamOPD}, a recipe combining verifiable streaming-video data, thinking-mode OPD, and instruct-mode deployment. It raises StreamingBench from $77.9\%$ to $83.9\%$---within $0.3$ points of the 9B teacher---and improves OVO-Bench excluding its hallucination-detection subtask (HLD) by $9.1$ points under unchanged inference. As a teacher-privilege extension, \emph{Spatio-Temporal CueGate (ST-CueGate)} aggregates cue-versus-no-cue teacher likelihood ratios into a group-relative response score that reweights OPD. It reaches $71.9\%$ on OVO-Bench (excluding HLD) and $64.9\%$ on Video-MME, and is the only variant that stays above the base model on all four benchmarks. Replacing the teacher with a frozen copy of the student's initial policy---on-policy self-distillation---retains most of these gains and lifts HLD to $57.0\%$, above both the untrained student and the 9B teacher, so abstention loss is not intrinsic to the recipe. We provide a transparent and reproducible reference for open-source streaming-video research.