Coupling a pretrained vision-language model (VLM) with a diffusion or flow-matching action expert has become the mainstream vision-language-action (VLA) paradigm for embodied policies, yet they remain unreliable once a task demands precise manipulation, e.g., submillimeter cable insertion. We attribute this weakness to a training objective that averages flow-matching errors across contexts and flow times, allocating little supervision to the few decisive moments determining task success. Along the generative path, inference integrates a locally supervised velocity field, so equally penalized errors at different flow times can affect the executed action unequally. Consequently, precision-task performance deteriorates as physical tolerance tightens by orders of magnitude. We call this supervision imbalance across contexts and flow times Flow-Time Starvation. The remedy is to jointly align supervision allocation and representation learning with context-dependent precision demand, enabling the policy to recognize when greater precision is needed. We instantiate this precision-forcing strategy as Precision-aware Reweighting and Internalization for Skilled Manipulation (PRISM), which scores precision demand offline, strengthens flow supervision where errors are consequential and action signals are visible, and internalizes that demand in the VLM condition representation. Simulation and real-robot experiments show that PRISM preserves or improves general-task performance while raising mean end-to-end success from 38.3% to 86.7% across drive connector insertion, bimanual connector mating, and screw tightening, substantially extending the precision boundary of existing embodied policies without new sensors or observation modalities.

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