You don't technically. The borrow checker doesn't effect the semantics of the program (like, for example, type inference does) and the rest of the compiler doesn't need to (and in fact, doesn't) use its analysis to figure out how to compile the code.

The downstream compiler does assume that the code followed the rules for accessing references - i.e. didn't violating aliasing rules. The borrow checker guarantees this, but it's fundamentally a conservative check. It rejects programs it can't guarantee are correct, and rice's theorem proves that there are always correct programs that it can't guarantee are correct.

That said if you just treat rust-references like C-pointers you will run into issues. The aliasing rules for rust references are stricter. Also not fully agreed upon yet - the currently closest to accepted definition is in the "tree borrows" paper but it has yet to be adopted as the official one by the rust team.