Not quite, there is code which fails borrow checking but is safe and sound.

That is part of why a number of people have been waiting for Polonius and / or the tree borrows model, most classic are relatively trivial cases of "check then update" which fail to borrow check but are obviously non-problematic e.g.

    pub fn get_or_insert (
        map: &'_ mut HashMap<u32, String>,
    ) -> &'_ String
    {
        if let Some(v) = map.get(&22) {
            return v;
        }
        map.insert(22, String::from("hi"));
        &map[&22]
    }

Though ultimately even if either or both efforts bear fruits they will still reject programs which are well formed: that is the halting problem, a compiler can either reject all invalid programs or accept all valid programs, but it can not do both, and the former is generally considered more valuable, so in order to reject all invalid programs compilers will necessarily reject some valid programs.