He did "own up", because the bill as it was written didn't have a "Life of the mother" clause.
Wrong! The bill, as written, had a "life of the mother" clause. It had NO "health of the mother" clause.
The law does, in fact, have a life of the mother exception:
This subsection [imposing penalties] does not apply to a partial-birth abortion that is necessary to save the life of a mother whose life is endangered by a physical disorder, physical illness, or physical injury, including a life-endangering physical condition caused by or arising from the pregnancy itself.
The courts have been striking it down on the fact that it doesn't have a "health of the mother" exception.
And, anyone who has studied the issue knows that partial birth abortion is never necessary to preserve either the life or the health of the mother.