I think that’s fair. I was using Ivy League loosely. The point I am trying to get across is that, for certain jobs and milieux in the USA, especially on the east coast, St Andrews is a good uni to have gone to.
Example, I have a brother in law in Manhattan in finance, and a brother of a different brother in law in Big Law in Charleston. Americans love and boost endlessly their alma maters. People this connected talking up St Andrews professionally is very helpful. On the flip side , Imperial, UCL or Durham don’t have any brand awareness.
For the next tier after Oxbridge, the courses may be as good or even better than Oxbridge, but the brand recognition is more niche. I would imagine an engineering degree from Imperial College would get a lot of kudos in China for instance. Or an economics degree from the LSE in Washington DC.
So no, nothing else is on par with Oxbridge in terms of international reputation, but the next tier is very, very good. And, that next tier is hard to put into a hierarchy because they have niche reputations that punch hardest in particular subjects and contexts.