Seeing as it's relevant here too, I'll c&p my post from another thread to further underline the point:
There is a lot the WT article missed out.
Regarding Ashuretel-ilani, while it is technically true this Assyrian king ruled 'in Babylonia' for four years, what the article doesn't disclose is that he only held one or two of the cities in Babylonia (principally, Nippur) while other cities had been taken over by Nabopolassar.
Similar can be said about Shin-sharra-ishkun. He ruled parts of Babylonia over a period of seven years. The Assyrian empire was in its death throes and there were power struggles between the Assyrian empire and the rising Neo-Babylonian one with cities being won and lost, lost and won. The WT article fails to make clear (deliberately, no doubt) that these kings Ptolemy omits shared the same regnal 'time space' with Nabopolassar. Ptolemy needed to assign one king to a particular year to be able to count and make his astronomical calculations. The inclusion of these competing Assyrian kings (who lost in the end) would have been superfluous to his purposes.