The tips and notes for the lesson on aspect says this about Klingon perfective:
As you know, the verb suffix -pu' marks perfective aspect: that a given action is completed. It's broadly equivalent to the English perfect tenses: "has done, had done, will have done".
Klingon perfective is not broadly equivalent to the English perfect tenses. It can commonly be translated using the English perfect tenses, but it's also true that it can commonly be translated using English simple past. Usually, both translations are valid. The Klingon Dictionary itself mentions commonly translating perfective into English perfect tenses, and then most of the time it translates using English simple past tense anyway. In isolated sentences, it's impossible to pick one that's better.
At the very least, "broadly equivalent" should be changed to "commonly translated into" or something like that. If perfective is explained earlier, as seems to be the case from that text, it should not be introduced there as "equivalent" to English perfect tenses either.