if this were true it would not be possible for the system to read the watermark.
You confuse "invisible to humans" with "invisible to statistical analysis". Humans can't, for example, see the difference between metameric colours. Statistical analysis can. Humans can't see minor drift at scales where Brownian motion dominates. Statistical analysis can. Humans can't see the difference between background disease rates and new rising threats. Statistical analysis can. On and on. Statistical analysis is a far more powerful tool than human perceptual abilities.
this is also a lie. Identical thoughts must be expressed identically, otherwise they are, in fact, *different* thoughts.
I literally gave an example above. If you saw "picked a mango", "selected and picked a mango", "from within the tree, picked a mango", you would never think there was anything going on in the choice, and it isn't going to change the story one iota.