How sound is the belief that whoever saves a drowning girl, she becomes his daughter and he is forbidden to marry her, and if it is a boy, he becomes his son?

Saving a drowning person or anyone facing perdition is a religious obligation, and it carries a great reward, for Allah Almighty says: "And whoever saves a life - it is as though he had saved all mankind." (Quran 5:32) It is not permissible in Islamic law for the rescued girl to become the daughter of the rescuer, or for the woman to become his mother. This constitutes adoption, which Islam has abolished and forbidden, for Allah Almighty says: "Nor has He made your adopted sons your [true] sons. That is [merely] your saying by your mouths, but Allah speaks the truth, and He guides to the [right] way. Call them by [the names of] their fathers; that is more just in the sight of Allah. But if you do not know their fathers, then they are your brothers in religion and your Mawalikum." (Quran 33:4-5)