The aim of this short note is to report on a counter-example by Stefano Aguzzoli (private communication) showing that a claim made in a recent paper of ours [2, Proposition 5.2], stating that the class of states of a free product algebra is closed, is in fact not true. That claim was used in turn in the proof of one of the main results of the same paper [2, Theorem 5.4]. However, we also provide in this note an alternative proof for that result, so that it keeps holding true.