A former Admissions Tutor here (although in the humanities). Another way of looking at it is that the DD in question didn't have the profile/predictions required' or didn't stand up to the competition for this particular course. Normally, an outright reject; however, in my Department, we'd not want to lose a potentially talented student, so might offer for a less sought-after or hard to get into course.
It's also a reasonable assumption to make that an applicant may be drawn to a particular university, as much as a specific course at that university. So it might be that a university will offer a cognate course because they are offering the applicant a chance to study at that university.
It's up to the candidate to accept or reject whatever offer they are made by a university. Some applicants want to study at the University of X in a broad area, so it's a standard recruitment practice.
I don't think there's been any arrogance or lying on Exeter's part. The OP's DD didn't have what they wanted for the course she applied for. They've offered her a reasonable alternative, in case she's one of those applicants with her heart set on Exeter. If she's not, that's not Exeter's problem or fault. Neither the applicant nor Exeter has lost anything here.
There has been considerable arrogance by the OP however. I wonder if she'd accuse a university admissions unit in person, without the cover of anonymity, of being arrogant liars?