I think that this is backwards: of course they could fill the spaces- if they wanted to. Amongst other things, Oxbridge take a lot of flack for giving medicine spaces to foreigners while turning away highly qualified citizens- so they only do it when somebody really catches their eye. Remember, these are state supported, not independent, institutions. It’s not a quota in the sense that they are supposed to fill it, it’s a ceiling that they may not exceed.
Also agree with @HazeGrey: AP/SAT scores are mostly a filter, and an assurance that a minimum level of competence in the subject has been achieved (and tbh, the standard of US education -and APs in general- is widely believed to be materially less than the UK standard- even though, as @HazeGrey & I have seen, our kids were well able for the level of work). The interview thing is also real: I have talked to tutors about the process, and there are a lot of variables that are not necessarily obvious (for example, does the applicant seem ‘teachable’ in the Oxford tutorial format)
It won’t satisfy your itch for Oxford ‘prestige’, but the University of Buckingham now has an independent medical school, which has no cap on student places. It’s a 5 year degree, and is pricey (~£30K/pa tuition + living), and they are only in year 2 (it launched in 2015), but it builds on a pre-existing base and is fully accredited. It is also competitive- they had 500 applicants for ~70 places in the first year; dk the numbers from the second intake year.