fairycakes It sounds like your DD will be fine for home student fees, but sending her to boarding school would not have made any difference, as she would have been considered only resident in the UK for purposes of education. It's likely she would have been informed if she might be considered an international applicant when offers were given (although this is not always the case).
WRT your original post, when applying to competitive courses at top universities, you have to accept there will be some rejections. The vast majority of applicants will have a strong academic profile, PS and reference, and the university have to differentiate somehow, and different universities have slightly different systems.
Also, it's worth bearing in mind that top universities that don't interview sometimes put more weight on the PS than Oxford will. You mention your DD's English in one post, so I wonder if there were some minor issues in her PS that might put an admissions tutor off? For most universities, the PS is the only bit of written English they see, and some universities might use this to judge the candidate's standard of English.
Ultimately, I do think some universities could be slightly more transparent with their admissions process, but equally, they can give whatever offer they like to whoever they chose, and different universities may have slightly different ideas about what they want from an applicant. Unless you have experience of universities admissions, this can be a bit of a shock- and it's generally why applicants are advised to NOT apply to 5 very competitive courses, even if they have excellent grades.