We show in detail that the Parikh-Wilczek tunneling method (PWTM), which was designed for resolving the information loss problem in Hawking radiation (HR) fails whenever the radiation occurs from an isothermal process. The PWTM aims to produce a non-thermal HR which adumbrates the resolution of the problem of unitarity in quantum mechanics (QM), and consequently the entropy (or information) conservation problem. The effectiveness of the method has been satisfactorily tested on numerous black holes (BHs). However, it has been shown that the isothermal HR, which results from the emission of the uncharged particles of the linear dilaton BH (LDBH) described in the Einstein-Maxwell-Dilaton (EMD) theory, the PWTM has vulnerability in having non-thermal radiation. In particular, we consider Painlevé-Gullstrand coordinates (PGCs) and isotropic coordinates (ICs) in order to prove the aforementioned failure in the PWTM. While carrying out calculations in the ICs, we also highlight the effect of the refractive index on the null geodesics.