black hole thermodynamics - Another limit on the fine structure constant - based on a formula by Lubos Motl

This paper by Hod entitled "Gravitation, thermodynamics and the fine-structure constant" (PDF) starts from a formula on black hole resonance frequencies. If you follow the references through, Lubos Motl has also derived this formula in L. Motl, Adv. Theor. Math. Phys. 6, 1135 (2003). Now Hod claims that the formula and the third principle of thermodynamics, taken together, imply that

$$\alpha > \frac {{\rm ln} \,3} {48 \, \pi}$$

This is a very good limit, because it means that $\alpha > 1/137.26$ - which is very close to the real value $1/137.036$. Is Hod's argument correct?