They can't, and "intact" watermarks don't show up. You're the one who is misunderstanding how this works.
When a pattern is present very frequently the AI can learn to imitate it, resulting in things that closely resemble known watermarks. This is called "overfitting" and is avoided as much as possible. But even in those cases, if you examine the watermark-like pattern closely you'll see that it's usually quite badly distorted and only vaguely watermark-like.