(Maybe you are basing that claim on something more than vibes. If so, show your work! What tests did you do? What were their results?)
First, I think it's worth distinguishing "had a false positive once" from "is no better than astrology".
Second, once it occurred to me that there might have been a famous false positive on the DoI, one of the first things I found in a web search was a lengthy discussion from the makers of Pangram (generally, I think, considered the best of them) about (1) why some AI-detectors think the DoI was AI-written and (2) why their software, which allegedly works a different way, doesn't.
I gave it a try. It was a couple of years ago that "look at these stupid AI detectors rating the DoI as AI-written" thing did the rounds, so they've probably all made sure that specific thing doesn't happen any more. So I tried a 100-word chunk of the US Constitution. (100 words because that's what you get per "credit" and I wanted to try it on some other texts too. The last two paragraphs of section 3 are 103 words and the last three words can be removed to leave a coherent sentence, so that's what I used.) It said: too short to classify with certainty, but 100% "possibly human". "High" confidence, whatever that means.
Well, maybe they fudged the DoI and thought to fudge the Constitution while they were at it -- in fact, maybe they do something like searching the web to check for possible human authorship. So my next test was a passage from a (printed) book, recent enough not to be in Project Gutenberg or the like, obscure enough that it's unlikely that people are quoting it a lot. ("Lessons from an Optical Illusion" by Edward Hundert, a paragraph from page 111. I had to truncate it a bit to fit into 100 words.) Once again: too short to be sure but 100% "possibly human", "high confidence".
Maybe they do have that book in some big internal database. So, next test: another printed book, but this time make some changes so that the text I give the detector doesn't exactly match the text of the book. This time I picked a novel by Charles Stross. ("Quantum of Nightmares", page 116 of the edition I have.) I changed names, synonymized words, and restructured sentences. Too short to be sure, 100% "possibly human", high confidence.
Maybe they just rate everything "possibly human". I asked Claude (Sonnet 5.5; I don't have a paid sub) to write me a couple of paragraphs of urban fantasy "a little in the style of Charles Stross". The chunk I gave it was 103 words and I decided not to mess with the text despite the extra 1 credit it would cost me. (I didn't want to take a _much longer_ chunk lest that introduce a bias -- maybe shorter pieces of text are more likely to be rated "possibly human".) 100% "possibly AI", high confidence.
My prompt to Claude had produced something thematically consistent with the original Stross, so I took ~50 words from its next paragraph along with ~50 words from Stross, again with serial numbers filed off by me. "46% of this text is possibly AI", quoth Pangram. It put the boundary exactly where it actually was. It says "low confidence" for the likely-AI bit and "high confidence" for the likely-human bit.
I'm sure Pangram is foolable (see e.g. https://freddiedeboer.substack.com/p/how-to-produce-a-pangra...) but 5/5 unambiguously correct results seems significantly better than astrology to me.