When you shoot across level terrain, the bullet starts out basically horizontal, so there's no vertical factor at the muzzle, and the drop is due entirely to the effect of gravity.
While this is an interesting explanation, it is incorrect.
* When a rifle is fired, the projectile leaves the muzzle in line with the bore, then begins to drop immediately due to G.
* When sighting in a rifle, you are trying to intersect two lines, the line of sight (along which you are looking through the sights) and the path of flight of the bullet (initially a line centered on the rifle bore line). These lines form a triangle with the apex at the point of impact/point of aim (assuming rifle is sighted POI/POA)
* When you shoot a rifle, the bullet leaves the muzzle converging with (travelling "upwards" to intersect) the line of sight at your sight-in distance.
* When you shoot with the line of sight level, the bullet leaves the muzzle travelling towards the line of sight. The bore is lower than your scope/line of sight so the bullet has to be aimed "up" in order to reach your point of aim.
* The bullet also drops during flight, so it is actually pointed a little higher than your POA when it leaves the muzzle.
* When shooting downhill at close range like the OP describes, the bullet has not yet crossed the line of sight, so it will hit lower than point of aim by about 1"-1.5".
* Assuming you are holding the rifle in the normal vertical position while shooting downhill, at longer ranges the bullet will strike higher than POA because its line of flight is affected by gravity multiplied by the sine of the angle.