It is a matter of relativity, meaning, the description of "which way the bullet moves" is relative to your point of view. And, of course, this sounds confusing...
Your line of sight is just that, a line. Back sight, front sight, target.
Case in point, rifle is shooting high, meaning bullets are hitting ABOVE the point of AIM. The line of sight goes to the point of AIM. The object is to move the line of sight, so it ends at the point of IMPACT, making the POA and POI the same.
TO do this, you need to raise the POA up to meet the POI. Since it is a line, to raise one end, you lower the other (rear sight goes down).
BUT, when you do this, what it looks like on the target is that the bullet impact
seems to move DOWN to the point of aim. In reality the bullet still hits in the same spot.
The people saying move sight opposite are looking at how you move the line of sight, the people saying move the same direction are looking at how the bullet appears to move on the target.
Both are actually correct, but only if you realize their frame of reference.
If its not as clear as mud, now, I can elaborate...