It should first be noted that the circle drawn derives from experimental results. If you were to mark specific oxygens, e.g. by introducing radioactive $\ce{^18O}$ in place of normal $\ce{^16O}$, you can predict whether and where the ester product will contain $\ce{^18O}$ or not and whether the water will contain $\ce{^18O}$ or not.
$$\begin{align}\ce{R-CO-OH + HO{*}-R &<=>> R-CO-O{*}-R + H2O}\\[0.5em]
\ce{R-CO{*}-O{*}H + HO-R &<=>> R-CO{*}-O-R + H2O{*}}\end{align} $$
Why this happens is due to the reaction mechanism. The mechanism’s first step is a nucleophilic attack of the alcohol oxygen to the $\ce{C=O}$ double bond to give a tetrahedral intermedate with $\ce{O-}$, $\ce{OH}$ and $\ce{HOR+}$ all bound to a single carbon. This breaks down by the $\ce{C=O}$ bond being formed and one group being expelled. If $\ce{HOR+}$ is expelled, the starting materials are regenerated. If $\ce{OH-}$ is expelled, then after proton transfer the ester product is generated.
Within this mechanism, there is never an attack on the alcoholic $\ce{C-O}$ bond so it cannot be broken. Furthermore, it is quite hard to break a $\ce{C-O}$ bond under displacement of $\ce{OH-}$ anyway. The only reason why it works in ester formation is that at the same time $\ce{C=O}$ is regenerated which provides the required energy.