Regression Line Method
Thought about a very simple example: Suppose we have two distinct points $(X_{1},Y_{1})$ and $(X_{2},Y_{2})$. The best regression line for these two points would be the line that passes through both points. However, any line passing through $(\frac{X_{1}+X_{2}}{2},\frac{Y_{1}+Y_{2}}{2})$ would let $\hat u_{1}+\hat u_{2}=0$, just like the perfect regression line.