That seems right to me although I think at the margins there are US public programs and UK programs that are getting pretty close. Speaking of which:
I can’t answer for every student but my S24 decided to scratch Oxbridge due to a combination of a lot more onerous application process plus the fact they are usually only three-year programs that leave even less room for exploration than the four-year Scottish equivalents.
St Andrews also has a far higher percentage of US students–it was something like 20% in the stats we saw, 2% at Oxford, less than 1% at Cambridge. St Andrews is also smaller, but even in gross terms I think there were over 6 times as many US students as Oxford, 16 times as Cambridge.
Obviously that could be a pro or con, or a matter of indifference, but I think my S24 felt some comfort in the fact that there would be a decent population of other US kids, and for that matter likely a decent population of US alums. In fact I forget the exact details, but I think we figured out St Andrews typically had more US students than Haverford (the smallest college on his list, but still).
Finally, it felt to him (and me) like St Andrews was sort of the Dartmouth of the UK in the sense that although it was a research university, it was at least more undergraduate focused than most. A lot contributed to that impression, but there is also just a raw numbers thing. So, like, I think something like 80% of St Andrews students were undergrads. Cambridge was just over 50%, and Oxford was just under 50%.
Anyway, his impression was ultimately that in some notable ways St Andrews was “closer” to the sort of US undergrad experience he was looking for. But to be fair, in the end he decided not close enough. Still, I think there are plausible scenarios in which he fell in love with St Andrews and went there despite never even applying to Oxbridge.