I believe, it is not mistranslated at all. The translation of a word would have to depend on its context. What we have is about translation, not a mere definition of a Greek word in English. Nevertheless, the KJV translators are correct to say because they knew pisteou is not to be translated uniformly as "believe". Actually, the KJV did not consider "believing" in the translation of pisteou.
Pisteou, according to the KJV has entirely 248x word usage translated in English as believe 239, commit unto 4, commit to (one's) trust 1, be committed unto 1, be put in trust with 1, be commit to one's trust 1, believer 1