Maybe not visually hidden, but practically invisible to human: imagine a text box with color #fffffe on a white background. Visually impossible to discern for most humans on most screens, but for a machine #fffffe is totally distinct from #ffffff, and fully visible if display != none.

As AI becomes more intelligent, you can prove humanity by exploiting our weaknesses.

(Another idea. Have a random image on a page actually be a text box with an image background. You cannot activate it if you focus on it, with your mouse or touch, but a bot doesn't need focus to change input.value.)