The moon waxing gibbous is a fun example - what if moon phase were to affect our biology in subtle ways?
There are plenty of things that people feel or know to be true but have trouble putting into words. That guy you know who just gives you a creepy vibe, but you can't put your finger on exactly why?
But there is also an extent to which if my example did occur, it would still be flawed, at least with modern AI. Even if all these signals are in some abstract sense truly signals that you are a terrorist, in the real world it is still not correct to simply add them together, or whatever other simple operation the AI is doing. For all that deep learning may be cool, it's still got some giant, gaping holes in it compared to however human cognition works. Humans can look at say "Yes, even if those are all 1% signals, it really isn't sensible to add them all together." The current state of AI is not able to come to that conclusion, or at least, not well enough.
If that changes in the future, well, I'll update my beliefs as appropriate then. It's hard to guess the "cognitive shape" the biases of the next breakthrough in AI may have.