A counterexample to the symmetric rank-two critical-point formula

Every hollow symmetric complex $3\times3$ matrix has the form $X(a,b,c)$ with off-diagonal entries $a,b,c$ and determinant $2abc$, so the variety of such matrices of rank at most two is the union of the three coordinate planes, and its smooth locus consists of the points with exactly one zero coordinate. For symmetric data with nonzero off-diagonal entries $\alpha,\beta,\gamma$, the bilinear full-Frobenius distance restricted to each plane has exactly one critical point, namely $(0,\beta,\gamma)$, $(\alpha,0,\gamma)$ and $(\alpha,\beta,0)$, and each restricted Hessian is $4I_2$, so all three are nondegenerate. Hence the generic number of critical points on the smooth locus is $e_{3,3}=3$, whereas the conjectured formula of Kubjas, Sodomaco and Tsigaridas predicts $27(3-3)+4=4$, and its universal assertion is false.