it's the same exact skill being used except one scenario rewards it more
Not quite; imagine a player has a jittery hand, thus consistently misses the pixel he wants to aim at by an average of 10 pixels into any direction. He wants to aim at the center of a 20 pixels sized head with a pinpoint accurate weapon. Instead, he slips as usual and hits a point 10 pixels away from the center of the head. Due to the pinpoint accurate weapon, the shot hits the 20 pixels sized head missing the center by 10 pixels. It is still a headshot.
In the next case, imagine the jittery player uses a weapon with a 20 pixels sized crosshair. He wants to aim at the center of the 20 pixels sized head again, but slips by 10 pixels. 50% of the 20 pixels sized crosshair is now outside the area of the 20 pixels sized head, meaning he will miss with a likelihood of 50%.
Now assume a player with perfect aim and a weapon with a 20 pixels wide crosshair. He aims at the center of the 20 pixels sized head, doesn't slip unlike the jittery one, and the shot hits despite the inaccuracy of the weapon because the crosshair perfectly overlaps the head.
The pinpoint accurate system does the jittery player a favor, because he is able to land shots he otherwise wouldn't. The perfectly aiming player is indifferent about pinpoint accuracy or the 20 pixels sized crosshair, because he hits either way.
Consequently, the pinpoint accurate system promotes careless shooting into the general direction of the head, whereas the system involving randomness requires special care to center the wide crosshair over an equally-sized area. The prior needs less skill, the latter needs more.