Overtaking another vehicle on a two-lane road can turn dangerous within a few seconds, especially when the gap to an oncoming vehicle is short or that vehicle is moving fast. Many driver-assistance systems rely on a simple, fast rule called the Overtake Safety Margin formula to decide whether an overtaking maneuver is safe, without running a full traffic simulation. This study checks the formula's reliability using a physics-based simulator that models three vehicles: the car overtaking, the car being overtaken, and the oncoming car. One million generated overtaking scenarios were evaluated using both the OSM formula and the kinematic simulator to identify cases where the formula classified a maneuver as SAFE while the simulator predicted an UNSAFE outcome. These mismatches, called blind spots, represented 3.98% of the evaluated scenarios and were concentrated in high oncoming-speed, short-gap situations, pointing to a specific weakness rather than random error. To catch these blind spots automatically, a small and efficient machine-learning model, a micro-transformer, was trained on the simulator's results. It reached 96.3% overall accuracy and correctly flagged 86.9% of the formula's blind spots, outperforming LightGBM, which detected 73.2%. The model's confidence scores were well calibrated, so they can be trusted to trigger an extra safety check when needed. An uncertainty-based search then used these confidence scores to find risky scenarios efficiently: 187 of the 500 most uncertain cases turned out to be unsafe, about 9.4 times more effective than random selection. Finally, the 30 highest-priority cases were replayed in the CARLA driving simulator, and 27 were confirmed to reproduce unsafe outcomes. Together, these results show that pairing a fast rule-based formula with a calibrated learning-based monitor can catch dangerous situations the formula alone would miss, supporting the safety documentation required for automotive safety-of-the-intended-functionality standards.