Record the meeting. Ask for permission and just say something like "I like to review the meeting after it's over to make sure I'm understanding things correctly." Great optics, and then you can just read through the transcript while listening to the recording later.
Feel free to say "let me think about that and get back to you." And then make sure you get back to the person. It's okay to admit you don't have an answer off the top of your head as long as you DO bring back an answer later.