I think it might actually be _the wrongdoing_ that really exposes you to legal liability.
Therefore it is not _the action_ of having a child that exposes the man to legal liability, it is verbally accepting and or acting as if the child is his (cases and situations vary greatly).
This is part of why saying "Sorry" is so heavily avoided in certain subcultures, because it accepts culpability.
You can end up with mountains of liability while doing nothing wrong. And doing plenty of things wrong while having no practical liability (due to leverage).
Frankly, it’s so common that lawyers often don’t even care about what actually happened, rather what can be spun/alluded to/proven.