Aiming at specific body parts isn't even done today with precision firearms. Police and military aim for centre of mass for the greatest hit probability. Aiming at the head, or at the hands or legs, means that you are aiming at a rapidly and erratically moving target with much smaller surface area. The torso is a much larger target that is less likely to move unpredictably - and even, accuracy drops in a live situation compared to a static target at a range. And remember, this is with modern firearms. Anything past 30m or so means that you're not going to get a bead on a specific body part, let alone try to hit it.
How does this compare to the Medieval period? Bows are less accurate than modern firearms, and were used at greater distances. In battle, direct shooting would likely have been used at distances under 70m (generalising across the armies and conflicts), in which case the best thing to aim for was one specific soldier and you might hit him.
This is the basis for traditional Korean archery shooting at a ~2m target around 145 metres away, to represent the ability to hit a horseman on a battlefield. In other armies, such as the English, archers would be shooting indirectly at distances over 100m, but they were very effective in direct shooting roles under 50m, where they could hit targets with more ease, and begin to aim at specific weaknesses in armour, such as eye slits. The "arrow storm" that is described in historical accounts of battles like Agincourt and Crecy, given the heavy draw weights of English war bows and the distances they crossed, combined with the descriptions of French footmen having to lower their heads to avoid being hit in the eyes, indicates that the arrows were more or less coming straight at them, not from above.
How pinpoint accurate these English archers were in hitting their mark is mostly exaggerated. Donald Featherstone in The Bowmen of England postulates that it is difficult to imagine weary archers being able to land their arrows in every crevice and gap in French armour. He also questions the account of the Genoese bowman who, at Crecy, waved his fist in anger at the English archers at 100 paces, and 20 archers shot at him - and when later discovered slain, had 18 shafts through his forearm. Incredible, and worthy of a tale, but hardly supported by any real evidence.
In reality, it is simply too difficult to aim at a single target, let alone a body part, at the distances archers normally fought at. More often, they were shooting at a body of troops, not a single trooper's body. Limbs would not be visible, and certainly not eyes. Given the movement of the target, and the effect of the wind, hits were mostly circumstantial. Anyone who suffered the fate of Harold Godwinsson was plain unlucky. In fact, a skilled archer - according to Prince Louis Napoleon centuries after the end of archery - should be able to hit their mark one in ten arrows at long distance. Equally interesting is General de Marbot, a commander under Napoleon Bonaparte, who dismissed the mounted Baskirs as outdated fighters, bemoaned that only one in ten arrows found their mark against the densely packed French infantry. If a 10% hit rate was the best and worst archers could do, it's highly unlikely that they were trying to aim for specific body parts.
What we therefore see is that such claims to perfect precision are exaggerations in historical accounts or myths and legends. In modern Olympic-style archery, a recurve shooter with sights, stabilisers and light carbon arrows is shooting at a DVD-sized spot on a stationary target. The top professional archers might be able to hit this spot ~80% of the time, without being under pressure and with modern equipment. A modern compound bow on the same target might be able to push it closer to 90%. Remember that this target is centre of mass, and specific body parts would be even smaller than this.
As a light-hearted conclusion, such claims to specific precision is also not uncommon in pop-history TV shows, such as Deadliest Warrior. I did a parody of this in my critical commentary, in which I was able to prove that an average modern archer (using a traditional bow) could hit specific body parts on command...at around 10 metres.