A Problem with Hidden Move Go
As I read the description in Sensei’s Library (your own link), hidden moves are not considered to be played on the board until they are revealed; you may like to think of the stone as still in a special pot with a label on it. So a not yet revealed stone cannot be captured or in atari. It can, however, be used to prevent a move your opponent tries to make.

In your example, the hidden stone is therefore not in atari: neither it nor your hidden stone are even on the board. You next move does not capture the hidden stone. The board (which I suppose you mean by ‘table’) is not wrong. No third person is required.