maybe if it was on your back????

If you wear the blade down, two things occur: One, the sharp edge of the blade is resting against the inside of the scabbard, which will lead to damage to both scabbard and blade. Secondly, yes, you can draw the sword when the blade is down - in fact, blade-down was more common when riding a horse. This is because when you draw a curved blade that way up, the natural movement is for your hand and the blade to go up. That's a good thing on a horse, because you don't end up cutting through your own mount, and you then have a heigh advantage for striking down. On the ground, having the blade up means that you can draw in several directions easily. The first draw you learn the blade ends up making a horizontal cut, but you can also end up cutting vertically or diagonally, the draw is compact (so you are less likely to hit walls, passers-by, ceilings), and you have several options available to adapt to the situation. There are simply fewer options when your first draw is forced into an upward movement, when the blade is down. It's also worth noting that the safety aspects of sword handling all point to having the blade up, so that if it's dropped, it's less likely to cut someone on the way past.

there are basically three positions of the saya as one draws the blade, while drawing the blade the saya is turned in the obi to perform a horizontal cut, or with the blade down for a upward cut, or from its origonal position to do a downward cut from jodan position, the saya is then turned to its position after cubiri and resheathing.

No you are not missing anything, In iaia the saya is turned in the obi during the drawing process depending on the cut being made. Once the cut is done and as you do chiburi the saya is agian turned to its origonal position for re-sheathing or noto. There are only eight cuts one needs to learn in kenjitsu. It is interesting to note that in iaia most all kata are done from a kneeling position, and the cuts lack power, In the toyama ryu the kata are done standing and the cuts are very powerfull, the diff. is that Toyama ryu is combat kenjitsu while Iaia is not.

All traditional sword arts teach this draw, the injury to ones hand can occure when one uses a sword of improper length for the user, it is vital that the sword fit you correctly, and that you have a qulified teacher to show you haw this is done correctly. In over 30 years of the study of Toyama ryu and Jikshin Muso Eshin ryu I have never seen an injury in class using this draw technique, I have seen however injury occure due to incorrect re-sheathing or noto during pratice.

yes I believe you are, Iaido is about controlled movements of drawing the sword from its scabbard, striking or cutting an opponent, removing blood from the blade, and then replacing the sword in the scabbard. Iaido is often used interchangeably with Battōjutsu, literally meaning "technique of drawing the sword".