Suppose that you and your friend, Mary, have just interviewed your ex-coworker, David, who wanted a job at your company. After he has left, Mary says something to you about him.
(1) Mary said, "Do you remember David?"
I replied, "He looks familiar."
She said, "At least fifteen years ago, we both worked with him at ABC Supermarket."
I said, "Right. I remember him now."
She said, "He was fired for swearing and spitting at our manager."
I said, "I remember that. I'm glad you brought that incident up."
Suppose that you are talking to your cousin that you need money to pay your rent.
(2) I said, "I lost my job six months ago. I'm running out of savings. What should I do?"
He said, "I wish I could help. I lost my job last month too. Don't worry. I remember that our uncle said he's always willing to help us with anything."
I said, "I'm glad you brought his words up."
Is it correct to say "brought that incident up" and "brought his words up"?