I would believe her.
But always remember the final decisions are very institutional. Excruciatingly so. The student and family have no control at this point. Revel in the fact you got this close. And that you got the nice letter. I’d be happy. Because what matters is that a kid is satisfied he really did his best, during hs and in the app, that he gave it his very best shot.
I agree with BKSquared that about 6000 could be Yale finalists. Not sure what “1 committee” means. Other comments from Ivies have similarly said final table is roughly 3x. But that’s distributed across all the sub areas. And different regions often display different strengths and, of course, different numbers of applicants and then finalists.
You will know soon. Best wishes.