own up to

リーダーズダイジェスト11月号のKidsコーナーにあった記事です。
I was trying to get my son to own up to knocking an ornament off the cupboard. He thought I hadn't seen him and kept denying it.
Exasperated, he exclaimed, "Who are you going to believe, me or your own eyes?"
子供の言う事は面白いですね。　ところで "own up to" 慣用句のようですが意味は何でしょうか？
慣用句は調べにくいのでまず "own" を辞書で見ると、
・Dictionary.com: to confess (often fol. by to, up, or up to): The one who did it had better own up. I own to being uncertain about that.
・American Herritage Dictionary: Confess, make a full admission, as in Come on, Tim, you'd better own upthat you lost the car keys. This idiom uses the verb own in the sense of "acknowledge."
"own up to" だけではなく own up/own to とも言うのですね。