It has nothing to do with reaction speed, and everything to do with collision algorithms. A target can only be hit if it's visible, and the higher frame-rate allows more frames where the target can be hit.
More detail: take the case of a projectile traveling between the player's weapon and a target that appears for n milliseconds, and a frame-rate r in frames/sec. The number of frames that target is visible, and hence can be hit by the projectile, is proportional to n * r. With a lower frame-rate, the target will be visible, and hence available to be hit, for fewer frames than it would with a higher frame-rate, reducing the chance of hitting the target.
LTT did a video on this a couple of years ago. But I'm lazy, and I'm not going to look it up.
No amount of careful planning will ever replace dumb luck.