TalkIn, I really don't think Exeter have any compunction to lie to you, you say she has four offers? You really need to calm down about this, no-one is lying to you, they are merely going through a process, it may do be the process as you deem fit, but they are going through it none the less.
Your daughter is the one who is applying.
No-one is doing this to hurt you.
I may be stepping beyond the bounds of the thread here, but (and I say this gently) do you think there is a possibility you are over-invested in you DD's University applications and therefore her life?
I only say this because I know you are a long-standing poster (as I am but I NC regularly) and I've seen many of your posts and they always seem pretty on the ball, I generally agree with your posts, but you seem to have lost sight here, your usual beam of reasonableness seems a little off.
A step back may be helpful, it's not your life, is there something you're overcompensating for here?