It sounds to me like she's tired of studying so hard and wants a break. She wants to enjoy university, let her hair down and start living a bit after all the years at school working so hard.
In which case, she is right that Cambridge or Oxford would not suit her. Durham probably wouldn't either.
My personal feeling is that you believe she has to go to these outstanding universities so she can succeed in life and this is the message you are giving her, which is putting the pressure on
Maybe she'd just be happy at a mid-level uni, where she has no pressure and can have fun!
I loved my middle of the road campus uni and am very pleased I turned down Durham. I got a chance to breathe, enjoy life and figure out who I was and what I wanted, away from home.
A couple of years after university I completed an MSc at a well known red brick, and went on to take a research post at Cambridge. I also subsequently obtained a doctorate. My undergrad, non pretentious, relaxed, caring, fun university was by far my favourite place and ironically, the teaching there far exceeded the offer at Cambridge (bar the one to one tutor groups they have) or where I completed my MSc.
Oxbridge is incredible for some, but my experience working at Cambridge was that many (there are obvious exceptions) people there are just normal people with privilege and not necessarily that bright. There are however, some very bright people at every university, even the old poly's you know!
In my opinion, good GCSE and A level grades don't make you bright. A good grade often just reflects hard work and sometimes privilege through tutors, private school etc...
Some very bright people get poor grades.
On my doctorate programme the student who had 4 A*s at A level really struggled. I got poor grades at A level but I have a high IQ (mensa level) and found it all very easy! Grades don't always dictate who is naturally smarter!
She's young, encourage her to go somewhere she can relax, have fun and figure her future out by herself! If she is genuinely smart, life will all work itself out!
You also might want to support her to work on her confidence a bit before she heads to uni.