> It explicitly does automatic global analysis
They appear to think that the borrow checker isn't achieved with type theory, but with some other technique ("global analysis").
Although, to be fair, my understanding of making a practical affine type checker is that things get kind of wonky if you do it purely logically. So practically you do some data flow analysis. Which is, I believe, what rust is doing. This also explains why MIR was such a big deal for certain issues with borrow checking. They ended up with a format that was easier to run a data flow analysis on, and that allowed the borrow checker to handle things like non-lexical lifetimes, etc.
[I've only read about such things. So I might have mis-remembered some of the details. However, this is my take on why someone might not call rust's advances purely type theoretic (even if they can be handwaved as type theory at a high level).]