It does depend on the course - there are some courses which Exeter shares jointly with Falmouth University - I believe Medicine is one of these courses, but someone feel free to correct me. So you do one year at Falmouth, one year at Exeter, and then back again.
If she is adamant that she is not on a course similar to this, then she needs to check where she applied - Exeter has 3 campuses. St Lukes, Exeter. Streatham, Exeter. and Penryn, Cornwall. She may have applied to the Cornwall campus without realising, since I believe it has lower entry requirements in general - I almost did this myself. This is STILL Exeter University, but obviously not in the city of Exeter, so she will graduate with an University of Exeter degree.
Leading on from this - her accommodation offer may be made by Falmouth University if she's in Penryn - the two universities share accommodation - so this may be some of what you're getting confused about.
If its neither of these things, and to be honest, even if this is the case, ring up - if she did apply to the Cornwall campus, and has the grades, she may be able to transfer to the Exeter campuses if that is what she wants, or at least find out what is going on.
I hope this resolves itself, and that you'll keep us updated on any developments!