I don't think that anyone is under the illusion that Zeteticism is science.
What exactly is wrong with the Zetetic method?
In simple words, the Zetetic method relies on the first hand experience of the observer rather than the predictive power of the model which tries to explain the studied phenomena.
Just as an example, in perfectly Zetetic fashion, you look at the sea from your window and see it flat. Then, in perfect Zetetic fashion, you see the Sun moving towards the horizon during dawn and falling under the horizon without stopping, changing course, or hinting that you are really seeing an illusion.
Everything until this point clearly (in a Zetetic fashion) shows that the Earth is flat and the Sun actually falls under Earth. But then, it is now evident that when you see the Sun under the Earth it is clearly seen close to the zenith in another location on Earth.
Which of the three Zetetic observations is wrong? All of the three observations is totally Zetetic, and therefore is correct. But at least one of them is wrong, so Zeteticism is internally paradoxical.