Single-ownership ("affine types") is a separate concept from a borrow checker. Your language doesn't need a borrow checker (or references at all) to benefit from single-ownership, though it may make some patterns more convenient or efficient.

I think it's the other way around - he's projecting rust as what he wants

Actually there's tree borrows now. https://www.ralfj.de/blog/2023/06/02/tree-borrows.html