Orthogonal design columns don't automatically make sums of squares uncorrelated

Suppose $Y_i=\beta_1X_{i1}+\beta_2X_{i2}+\varepsilon_i$ where $E(\varepsilon_i)=0, \operatorname{Var}(\varepsilon_i)=\sigma^2$, $i=1,2,3$ and $X_{i1}=i-4, i=1,2,3$; $X_{i2}=i-2, i=1,2$ and $X_{i2}=i$ for $i=3$. A least-squares fit is carried out and sum of squares are calculated then: