I have never come across this, and a cursory search revealed no source for the claim other than this particular document. Succession struggles were certainly a feature of both the Achaemenid and Sasanian Empires (more so the latter, perhaps). However, "anarchy" following the death of a king actually sounds far more like post-Seljuk Persia (with Turkic traditions of succession struggles being entrenched), in particular, the Persia around the time the document was written. One of the most dangerous periods for minorities living in the Qajar dynasty, such as Zoroastrians, was precisely the time between the death of one king and the ascension of the next, since they were then at the mercy of local authorities. Assuming the authors of the document didn't just make this up, it's possible that political struggles in contemporary Persia could have inspired this idea one way or another.

My Spanish is pretty bad, so I have to rely on Google translate - if you come across any more specific reference than to "Ancient Persia", that might help me get to the bottom of it.