Why would such a thought even occur to a three year old?
It could happen. Kids say the darnedest things.
The problem’s not that the three year old made this remark, but that the mother took this as a trigger to do her utmost to screw up the child for life. This woman is a very disturbed and dangerous person who ought to be prosecuted for felony child abuse.
It wouldn’t. It’s a tacqiya-style lie.