Summary: We describe the simplicial complex \(\Delta\) such that the initial ideal of the binomial edge ideal \(J_{\mathrm{G}}\) of \(G\) is the Stanley-Reisner ideal of \(\Delta\). By using \(\Delta\) we show that if \(J_G\) is \((S_2)\), then \(G\) is accessible. We also characterize all accessible blocks with whiskers of cycle rank 3 and we define a new infinite class of accessible blocks with whiskers for any cycle rank. Finally, by using a computational approach, we show that the graphs with at most 12 vertices whose binomial edge ideal is Cohen-Macaulay are all and only the accessible ones.