That was true for earlier radar guided missiles. The latest ones are smart enough to account for distance and calculate an energy optimized intercept course rather than just pointing straight at the target.
The underlying principle of proportional navigation, which is what the first few generations of IR missiles use to navigate, is constant bearing decreasing range. If a missile maintains absolute bearing to a target, it will collide with that target. The first generation AIM-9, which was the first useful IR missile, didn't aim "slightly ahead" of its target, it pointed itself at the exact point where it would collide with its target, assuming the target was moving at constant speed in a straight line.
The spinning sensor that you mention was on a gimbal, it wasn't pointing along the boresight. The spinning caused it to act as a gyroscope, so it would maintain its orientation in absolute space. The gimbal would track the sensor so that it was pointing at the target, and the same inputs were fed into both the gimbal and the missile's control surfaces. Therefore, if the bearing was changing, that would cause the missile to maneuver in such a way that the bearing would stop changing. If the bearing wasn't changing, the missile would not maneuver. This is all you need to do to point the missile at the exact point where it will intercept a non-maneuvering target.
As a first order approximation, the assumption of a constant speed straight line target is a useful one, given the technological limitations of the time.
https://en.wikipedia.org/wiki/Proportional_navigation
https://en.wikipedia.org/wiki/Constant_bearing,_decreasing_r...
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