Translation:This alien was born three thousand years ago.
From what I've seen in this course there is a pretty consistent relationship between using the -pu' suffix and getting a translation that uses "has been", "had been" or "will have been". While it seems that this translation is perfectly reasonable, a student who uses this course as their primary means for studying tlhIngan Hol might be confused. Worth a thought anyway. :)
You are absolutely correct. The reason they do this is because Okrand himself used the sentence loSmaH ben jIboghpu' I was born forty years ago. They allow this without explanation or justification.
The real reason is, of course, that -pu' is not a perfect tense; it is perfective aspect, which is a different concept. It indicates that the action described is completed. It does not indicate that the action described happened "before" anything. Most of the time, a verb that is not marked as completed or continuous is specifically neither completed nor continuous.