I used to shoot a recurve some in college. My brother's taking up bowhunting w. a compound, and I've been teaching him the same draw I was taught
(Bow hand is above eye level as you "expand" you back, and bring it down to the target.)

However, on most of the hunting shows I've seen, they seem to use an awkward looking draw that starts a little low, and then comes up... and relies heavily on the bicep... Is there a reason to draw like this, or just a lack of training?

The reason for the draw starting low is primarily a safety one. Drawing your bow with the line of sight facing up is dangerous as if the arrow is released it can travel very far. In the first instance you only hit the ground in front of you. safety must always be considered first.

Having said that, the draw to the compound in an upright straight draw. I point my bow directly at the target that I intend shooting and draw in a very straight line - that gets my back tension in from the very start.

The correct technique is important from the start as the draw becomes automatic and bad form quickly entrenches itself.

Good luck and happy hunting

Same here. For hunting my compound is straight out in front of me during the draw. The less movement you make the better. My bow doesn't move a bit during the draw.
In fact if he has to point it up in the air to draw, shake and grunt, etc., then the draw weight is probably to high for hunting. He should be able to draw it smoothly and quietly back and hold for a bit. Practicing from a kneeling, and sitting positions is also recommended to better duplicate actual shooting in the field. Probably less than half the shots I have ever taken were from an 'ideal' standing position as at the practice range, all relaxed and on level ground so to say.
Anyway, my 2 cents.

Any time you draw without being in line with the target you throw your whole form off. Bringing the bow back in line after drawing either up in the air or down at the ground throws everything off and you will not shoot as good.