Without allowing the second AoO, Hold the Line is not useful at all for someone with a reach weapon against someone without one. In fact, it's absolutely worthless because you get the AoO anyway. Considering the case where you have the same reach as the person who is charging, Hold the Line provides the exact same benefit whether you have a reach weapon or not.
So, is the intent of Hold the Line to improve the ability of any defender except those with reach weapons, where they should have the advantage? I argue no. Your interpretation is yes, correct?