Every open house script you have been handed is built on capturing details at the door. She captures none of them and gets the appointment instead, which is the thing the phone number was only ever standing in for.
She ran open houses for years and collected nothing at the door.
"i never had a sign-in sheet. i never asked for their number."
What she brought instead was a printed list of comparable homes for sale nearby. When a visitor made it clear the house wasn't for them, she offered to show them one from the list that same day: "give me like 20 minutes and I'll meet you over there."
The phone number came out of arranging the meeting.
“So it was always about I never had a sign-in sheet. I never asked for their number.”
The sign-in sheet asks the visitor to give you something before you've given them anything — at the exact moment they've decided they don't like the house.
She gives first, and what she gives is the only thing that person wants right then: another house to see. They're already dressed, already driving, already in the neighborhood. The contact details arrive because there's finally a reason for them to exist.