This work studies trustworthy use of large language models for remote sensing satellite downlink scheduling. Rather than accepting a generated optimization model at face value, we organize the workflow into three guarded steps: candidate generation, benchmark-based validation, and fallback exact solving. The core technical component is a global time-slicing validator that converts visibility windows into atomic intervals; so, mutual exclusion at the ground-station side, mutual exclusion at the satellite side, and per-satellite download caps can be checked in a physically faithful manner. Results on a prototype instance indicate that LLM-based modeling can be integrated into a dependable scheduling pipeline when external verification and recovery are built into the loop.