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Unfortunately, the paper is sparse in statistical details, but I presume the cutoff value indicated was chosen as to maximize the Youden's J statistic (lr.eta). Without positive evidence that this is the method that was used, it has problems because the cost ratio varies with prevalence, as in this article kindly shared by @Scortchi. Similarly, the use of ROC curves to determine a threshold was considered "nonsensical" by David Hand because "the weight distribution over cost ratios, implicitly used in calculating the AUC, depends on the empirical score distribution."

Unfortunately, the paper is sparse in statistical details, but I presume the cutoff value indicated was chosen as to maximize the Youden's J statistic (lr.eta). Without positive evidence that this is the method that was used, it has problems because the cost ratio varies with prevalence, as in this article kindly shared by @Scortchi.

Unfortunately, the paper is sparse in statistical details, but I presume the cutoff value indicated was chosen as to maximize the Youden's J statistic (lr.eta).

One may conclude that the ratios that predicted a large diameter of the canal (and therefore could act as good indicators as to the absence of canal stenosis were not considered in the study, because no simple transformation was applied to for instance SL/VB (in yellow) to flip it onto the upper triangle:

Unfortunately, the paper is sparse in statistical details, but I presume the cutoff value indicated was chosen as to maximize the Youden's J statistic (lr.eta). Without positive evidence that this is the method that was used, it has problems because the cost ratio varies with prevalence, as in this article kindly shared by @Scortchi. Similarly, the use of ROC curves to determine a threshold was considered "nonsensical" by David Hand because "the weight distribution over cost ratios, implicitly used in calculating the AUC, depends on the empirical score distribution."

One may conclude that the ratios that predicted a large diameter of the canal (and therefore could act as good indicators as to the absence of canal stenosis) were not considered in the study, because no simple transformation was applied to for instance SL/VB (in yellow) to flip it onto the upper triangle:

After @Carl's observation about the fact that the positive correlation of SL/VB with the canal diameter of $0.652$ does not jibe with the concave curve and low AUC, the point (3) is reinforced - they are throwing in the same bag and comparing measures of wide cervical canal (healthy) with a positive correlation together with a measure of narrow canal (disease) with the only negative correlation: