Double-logarithmic finite-size scaling behavior of the specific heat does not necessarily imply its divergence

In a recent paper [Phys. Rev. E 60, 3823 (1999)] Mazzeo and Kuhn presented very careful analyses of the finite-size scaling (FSS) data obtained from the numerical transfer matrix technique. In this report, as a complement to that paper, a critical argument based on numerical evidence is given against the conventional interpretation of the FSS behavior of the specific heat. The argument is likely to cast doubt on previous claims for numerical evidence for the scenario of a logarithmic correction.