And I'm sure we've all seen what happens if you run the Declaration of Independence or the Gettysburg Address or the book of Genesis through an AI "detector". They usually come back as AI.

Only for poor quality systems. Unfortunately there are many systems that tried to make easy hype, but are the equivalent of an ML 101 classifier class project.

If one measures for perplexity (how likely text is under a certain language model), common text in a training set will be very likely. But you can easily create better models.