Training-free camera control for pretrained flow-matching video generators is a partial-observation inverse problem: a depth-warped guidance video supplies noisy evidence on a subset of latent sites, which the sampler must reconcile with the pretrained prior. Existing methods struggle to balance the trade-off between trajectory adherence and visual quality and the heuristic guidance-strength tuning lacks robustness. We propose \textbf{$h$-control}, which resolves this dilemma through a structural change to the sampler: each outer hard-replacement guidance step is augmented with an inner-loop \emph{block-conditional pseudo-Gibbs refinement} on the unobserved complement at the same noise level, with provable convergence to the partial-observation conditional data law. To accelerate convergence on high-dimensional video latents, we exploit their conditional locality, partitioning the unobserved complement into 3D patches, each tracked by a custom mixing indicator that adaptively freezes converged patches. On RealEstate10K and DAVIS, \textbf{$h$-control} attains the best FVD against all seven training-free and training-based competitors, outperforming every training-free baseline on every reported metric.