In my understanding the Aimpoint is not truly 100% parallax free despite claims to the contrary.
Aimpoint says that most red dot sights will exhibit angular deviation between the optical and mechanical axes of the sight when you shift your eye position away from the center of the sight:
Note that because of this angular deviation, the greater the distance to your target, the greater the shift in POI from POA.
Aimpoint's design, conversely, keeps the optical and mechanical axes parallel even when you shift your eye position:
Presumably this is why Aimpoint claims it to be parallax free. Note that despite the fact that the optical axis remains parallel to the mechanical axis, the POI still shifts by the amount you move your eye. The shift isn't much (+/- 15 mm from center for a 30 mm diameter tube), but it is there. However, in contrast to the design shown in the first diagram, the Aimpoint's shift in POA/POI does not get worse as distance to target increases because the optical and mechanical axes are parallel.
That is why people will say that the Aimpoint is effectively parallax free beyond 25-50 yards or so. At greater distances the offset induced by moving your eye becomes negligible when measured in angular MOA. For example, a 15 mm offset at 50 yards is roughly 1 MOA, already small compared to the 4 MOA diameter of the Aimpoint dot. Furthermore, an absolute offset of 15 mm maximum at any distance is truly negligible for the intended use of Aimpoints - combat and hunting of medium to large game.
Try comparing your Aimpoint to your laser on a target that is further away and see if the parallax error becomes negligible.
To read more about Aimpoint's design, go
here<edited to replace original background color of Aimpoint's graphics with an easier to see color>