Let \({\mathfrak B}\) be a \(C^*\)-algebra with Stratile-Voiculescu masa \({\mathfrak D}\) and \({\mathfrak A}\) be a maximal triangular subalgebra of \({\mathfrak B}\) with diagonal \({\mathfrak D}\). In the article [\textit{J. R. Peters}, \textit{Y. T. Poon} and \textit{B. H. Wagner}, J. Oper. Theory 23, 81-114 (1990; Zbl 0717.46050)] it is shown that \({\mathfrak A}\) need not be a \(C^*\)- subdiagonal subalgebra of \({\mathfrak B}\) (in the sense of Kawamura and Tomiyama). The authors investigate and explain this phenomenon from the perspective of groupoid \(C^*\)-algebras by representing \({\mathfrak A}\) as the ``incidence algebra'' associated with a topological partial order.