Indeed you cannot rule out astrology on information-density grounds. Astrology involves quite a lot of information, the problem is that it's mostly unrelated to the outcomes of interest. To get back to the information-density of text, "I love you" doesn't contain a lot of information, but it does contain the one bit you care about, because someone who loves you is more likely to say it than someone who doesn't.

So if you want to determine whether something was written by a human or by AI, to do better than chance it's enough for there to be a difference in the probabilites of a human writing it and AI writing it, respectively. Whether the resulting accuracy is good enough for a particular use case is another matter. 99% is pretty good odds for love and pretty bad odds for "am I going to survive today?" Hopefully there won't be a death penalty for posting AI-generated content.