A paper entitled "Erratum: "Existence and asymptotic stability for the semi-linear wave equation with boundary damping and source term" [J. Math. Phys. 49, 053511 (2008)]" was published in 2009 [2], in the Journal of Mathematical Physics. In the 2008 version [1], the authors prove a Theorem 2.3 under an hypothesis (2.3). This hypothesis concerns that a given function µ involved in the equations satisfies three inequalities together with some regularity assumption. In the Erratum, the authors mentioned "Hypothesis 2.3 on p. 053511-3 is not suitable." They explained that the two first inequalities in (2.3) "cannot be used together." The Erratum further corrects the assumptions of Theorem 2.3: the original assumption (2.3) is replaced by a new hypothesis, still denoted by (2.3), where the second original inequality has been replaced by a modified inequality. The Erratum then presents the arguments to correct the proof of Theorem 2.3 thanks to this new assumption. In the present document we prove that: 1. The new assumptions (2.3) cannot be satisfied: the two first inequalities are basically contradictory with the third inequality, but the third inequality can be dropped. 2. The claim that the Erratum corrects the proof of Theorem 2.3 is flawed: the required property on µ' is: µ' is bounded away from 0 and not that µ' is bounded. We then prove that the requirement that µ' has to be assumed to be bounded away from 0 is basically contradictory with the two first assumptions on µ in the new assumption (2.3), so that keeping only the two first inequalities of (2.3) does not allow to correct the proof of Theorem 2.3. Hence we show that the Erratum contains two major flaws, and through a deeper short analysis we establish that the proof of Theorem 2.3 cannot be corrected in this 2009 Erratum nor in the 2008 original version of the proof. As a consequence, Theorem 2.3 remains unproved.