The borrow checker is only one component of the means by which Rust statically enforces thread safety. If you design a language that doesn't allow pointers to be shared across threads at all, then you wouldn't need a borrow checker. Likewise if you have an immutable-only language. What's interesting about Rust is that it actually supports this safely, which is still unbelievable sometimes (like being able to send references to the stack to other threads via std::thread::scoped).
You may have to define your terms more carefully and extend past "doesn't allow pointers", but it can be true. Look to Erlang; the key to Erlang's safety isn't actually its immutable values, but the fact that no messages can travel between the various "processes" (threads in conventional parlance, just not "OS threads") that carry any sort of reference or pointer is what makes it so Erlang is safe without any concept of borrow checking. It also semantically copies all values (there are some internal optimizations for certain types of values that make it so they are technically not copied, but at the language level, it's all copies) and each process is GC'd, so in terms of the Rust borrow checker I mention this only in the context of cross-thread sharing safety.
But in general, if threads can't communicate any sort of pointer or reference that allows direct, unmediated access to the same value that some other thread will see, there's no need for a "borrow checker" for thread safety.
(Note that "but what if I have a thing that is just a token for a value that people can potentially read and write from anywhere?" is not an exception to this, because in this context, such access would not be unmediated. This access would still require messages to and from the "holding" process. This sort of safety won't stop you from basically deliberately re-embedding your own new sorts of races and unsafe accesses in at the higher level of your own code, it just won't be a data race in the same way that multiple threads reading and writing through the same pointer is a data race at the lower level. The main solution to this problem is "Doctor, it hurts when I do this." -> "Don't do that.")
Let me clarify: "wouldn't need a borrow checker for the specific requirement of ensuring thread safety". Clearly the borrow checker is quite useful in single-threaded contexts on its own. :P The point is just that it's perfectly valid to have a language that doesn't have "reference semantics" at all.
